अनुक्रम \(7,12,17,22,\ldots\) का सामान्य पद \(a_n\) क्या होगा?
What is the general term \(a_n\) of the sequence \(7,12,17,22,\ldots\)?
#sequences-general-rule-class9
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A (5n+2)
B (5n+7)
C (7n+5)
D (12n-5)
Explanation opens after your attempt
Step 1
Concept
This is an arithmetic sequence with common difference (5). In exams, use first term and difference in (a_n=a+(n-1)d).
Step 2
Why this answer is correct
The correct answer is A. (5n+2). This is an arithmetic sequence with common difference (5). In exams, use first term and difference in (a_n=a+(n-1)d).
Step 3
Exam Tip
यह समान्तर अनुक्रम है जिसमें अंतर (5) है। परीक्षा में पहले पद और अंतर से (a_n=a+(n-1)d) लगाएं।
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अनुक्रम \(7,13,19,25,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(7,13,19,25,\ldots\)?
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#explicit-rule
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A \(a_n=6n+1\)
B \(a_n=7n-1\)
C \(a_n=6n-1\)
D \(a_n=n+6\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=6n+1\)
Step 1
Concept
The first term is (7) and the difference is (6) so \(a_n=6n+1\). In exams check the first term by putting (n=1).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=6n+1\). The first term is (7) and the difference is (6) so \(a_n=6n+1\). In exams check the first term by putting (n=1).
Step 3
Exam Tip
पहला पद (7) और अंतर (6) है इसलिए \(a_n=6n+1\) है। परीक्षा में (n=1) रखकर पहला पद जाँचें।
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अनुक्रम \(5,12,23,38,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(5,12,23,38,\ldots\)?
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A \(a_n=n^2+4n\)
B \(a_n=3n^2-1\)
C \(a_n=2n^2+n+2\)
D \(a_n=7n-2\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=2n^2+n+2\)
Step 1
Concept
\(2n^2+n+2\) gives (5,12,23,38). In exams test the rule on the first four terms.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=2n^2+n+2\). \(2n^2+n+2\) gives (5,12,23,38). In exams test the rule on the first four terms.
Step 3
Exam Tip
\(2n^2+n+2\) से (5,12,23,38) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें।
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यदि \(a_n=4n^2-3n+2\) है तो \(a_5\) क्या होगा?
If \(a_n=4n^2-3n+2\), what is \(a_5\)?
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A (87)
B (72)
C (91)
D (83)
Explanation opens after your attempt
Step 1
Concept
Putting (n=5) gives \(4\cdot25-15+2=87\). In exams, substitute (n) directly and carefully.
Step 2
Why this answer is correct
The correct answer is A. (87). Putting (n=5) gives \(4\cdot25-15+2=87\). In exams, substitute (n) directly and carefully.
Step 3
Exam Tip
(n=5) रखने पर \(4\cdot25-15+2=87\) मिलता है। परीक्षा में (n) का मान सीधे और सावधानी से रखें।
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यदि \(a_n=9n-5\) है तो \(a_{11}\) का मान क्या होगा?
If \(a_n=9n-5\) then what is the value of \(a_{11}\)?
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A (92)
B (94)
C (96)
D (98)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=9\times11-5=94\). In exams multiply first and then subtract the constant term.
Step 2
Why this answer is correct
The correct answer is B. (94). \(a_{11}=9\times11-5=94\). In exams multiply first and then subtract the constant term.
Step 3
Exam Tip
\(a_{11}=9\times11-5=94\) है। परीक्षा में पहले गुणा करें फिर स्थिर पद घटाएँ।
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यदि \(a_n=3n^2-2n+4\) है तो \(a_6\) का मान क्या होगा?
If \(a_n=3n^2-2n+4\) then what is the value of \(a_6\)?
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A (96)
B (100)
C (104)
D (108)
Explanation opens after your attempt
Step 1
Concept
\(a_6=3\times36-12+4=100\). In exams write the square part and subtraction separately.
Step 2
Why this answer is correct
The correct answer is B. (100). \(a_6=3\times36-12+4=100\). In exams write the square part and subtraction separately.
Step 3
Exam Tip
\(a_6=3\times36-12+4=100\) है। परीक्षा में वर्ग वाला भाग और घटाव अलग-अलग लिखें।
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अनुक्रम \(3,9,19,33,\ldots\) के लिए सही सामान्य नियम कौन सा है?
Which general rule is correct for the sequence \(3,9,19,33,\ldots\)?
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A \(n^2+2n\)
B \(2n^2+1\)
C \(n^2+n+1\)
D \(3n^2\)
Explanation opens after your attempt
Correct Answer
B. \(2n^2+1\)
Step 1
Concept
For (n=1,2,3,4), \(2n^2+1\) gives the given terms. While checking options, match the first four terms.
Step 2
Why this answer is correct
The correct answer is B. \(2n^2+1\). For (n=1,2,3,4), \(2n^2+1\) gives the given terms. While checking options, match the first four terms.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर \(2n^2+1\) से दिए गए पद मिलते हैं। विकल्प जांचते समय पहले चार पद मिलाना उपयोगी है।
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अनुक्रम \(58,51,44,37,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(58,51,44,37,\ldots\)?
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A \(a_n=58-7n\)
B \(a_n=65-7n\)
C \(a_n=7n+51\)
D \(a_n=65+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=65-7n\)
Step 1
Concept
At (n=1) it gives (58) and at (n=2) it gives (51) so \(a_n=65-7n\). In exams treat the difference as negative in decreasing sequences.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=65-7n\). At (n=1) it gives (58) and at (n=2) it gives (51) so \(a_n=65-7n\). In exams treat the difference as negative in decreasing sequences.
Step 3
Exam Tip
(n=1) पर (58) और (n=2) पर (51) मिलता है इसलिए \(a_n=65-7n\) है। परीक्षा में घटते अनुक्रम में अंतर को ऋणात्मक मानें।
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अनुक्रम \(4,15,34,61,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(4,15,34,61,\ldots\)?
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A \(a_n=4n^2-n+1\)
B \(a_n=3n^2+1\)
C \(a_n=n^2+10n-7\)
D \(a_n=11n-7\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=4n^2-n+1\)
Step 1
Concept
Using \(4n^2-n+1\) gives (4,15,34,61). In exams check a quadratic rule when second differences are constant.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=4n^2-n+1\). Using \(4n^2-n+1\) gives (4,15,34,61). In exams check a quadratic rule when second differences are constant.
Step 3
Exam Tip
\(4n^2-n+1\) रखने पर (4,15,34,61) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम देखें।
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यदि किसी अनुक्रम का नियम (a_n=3n+(-1)^n) है तो पहले चार पद कौन से होंगे?
If the rule of a sequence is (a_n=3n+(-1)^n), what are the first four terms?
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A (2,7,8,13)
B (4,5,10,11)
C (2,5,8,11)
D (3,6,9,12)
Explanation opens after your attempt
Correct Answer
A. (2,7,8,13)
Step 1
Concept
((-1)^n) gives (-1) for odd (n) and (1) for even (n). In exams, check odd-even positions in alternating rules.
Step 2
Why this answer is correct
The correct answer is A. (2,7,8,13). ((-1)^n) gives (-1) for odd (n) and (1) for even (n). In exams, check odd-even positions in alternating rules.
Step 3
Exam Tip
((-1)^n) विषम (n) पर (-1) और सम (n) पर (1) देता है। परीक्षा में वैकल्पिक चिह्न वाले नियम में (n) की सम-विषम स्थिति देखें।
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यदि \(a_n=4n+7\) है तो कौन-सा पद (75) के बराबर होगा?
If \(a_n=4n+7\) then which term is equal to (75)?
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A (n=15)
B (n=16)
C (n=17)
D (n=18)
Explanation opens after your attempt
Step 1
Concept
From (4n+7=75) we get (n=17). In exams equate the formula to the given value to find the term number.
Step 2
Why this answer is correct
The correct answer is C. (n=17). From (4n+7=75) we get (n=17). In exams equate the formula to the given value to find the term number.
Step 3
Exam Tip
(4n+7=75) से (n=17) मिलता है। परीक्षा में पद संख्या के लिए सूत्र को दिए मान के बराबर रखें।
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यदि \(a_n=5n+3\) है तो कौन-सा पद (88) के बराबर होगा?
If \(a_n=5n+3\) then which term is equal to (88)?
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A (n=15)
B (n=16)
C (n=17)
D (n=18)
Explanation opens after your attempt
Step 1
Concept
From (5n+3=88) we get (n=17). In exams equate the formula to the given value to find the term number.
Step 2
Why this answer is correct
The correct answer is C. (n=17). From (5n+3=88) we get (n=17). In exams equate the formula to the given value to find the term number.
Step 3
Exam Tip
(5n+3=88) से (n=17) मिलता है। परीक्षा में पद संख्या के लिए सूत्र को दिए मान के बराबर रखें।
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अनुक्रम \(-2,3,8,13,\ldots\) का (20)वां पद क्या होगा?
What is the (20)th term of the sequence \(-2,3,8,13,\ldots\)?
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A (88)
B (93)
C (98)
D (103)
Explanation opens after your attempt
Step 1
Concept
This is an arithmetic sequence and (a_n=-2+(n-1)5). Putting (n=20) gives (93).
Step 2
Why this answer is correct
The correct answer is B. (93). This is an arithmetic sequence and (a_n=-2+(n-1)5). Putting (n=20) gives (93).
Step 3
Exam Tip
यह समान्तर अनुक्रम है और (a_n=-2+(n-1)5) है। (n=20) रखने पर (93) मिलता है।
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अनुक्रम \(9,17,25,33,\ldots\) में (81) कौन-सा पद है?
In the sequence \(9,17,25,33,\ldots\) which term is (81)?
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A आठवाँ पद / (8)th term
B नौवाँ पद / (9)th term
C दसवाँ पद / (10)th term
D ग्यारहवाँ पद / (11)th term
Explanation opens after your attempt
Correct Answer
D. ग्यारहवाँ पद / (11)th term
Step 1
Concept
Its rule is \(a_n=8n+1\) and (8n+1=81) gives (n=10). In exams recheck the calculation before choosing the option.
Step 2
Why this answer is correct
The correct answer is D. ग्यारहवाँ पद / (11)th term. Its rule is \(a_n=8n+1\) and (8n+1=81) gives (n=10). In exams recheck the calculation before choosing the option.
Step 3
Exam Tip
इसका नियम \(a_n=8n+1\) है और (8n+1=81) से (n=10) नहीं बल्कि (n=10) मिलता है। परीक्षा में विकल्प चुनने से पहले गणना दोबारा जाँचें।
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अनुक्रम \(111,102,93,84,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(111,102,93,84,\ldots\)?
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A \(a_n=111-9n\)
B \(a_n=120-9n\)
C \(a_n=9n+102\)
D \(a_n=120+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=120-9n\)
Step 1
Concept
At (n=1) it gives (111) and at (n=2) it gives (102) so \(a_n=120-9n\). In exams keep the decreasing difference negative.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=120-9n\). At (n=1) it gives (111) and at (n=2) it gives (102) so \(a_n=120-9n\). In exams keep the decreasing difference negative.
Step 3
Exam Tip
(n=1) पर (111) और (n=2) पर (102) मिलता है इसलिए \(a_n=120-9n\) है। परीक्षा में घटते अंतर को ऋणात्मक रखें।
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यदि \(a_3=14\) और \(a_8=39\) किसी समान्तर अनुक्रम में हैं तो सामान्य पद \(a_n\) क्या होगा?
If \(a_3=14\) and \(a_8=39\) in an arithmetic sequence, what is the general term \(a_n\)?
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A (4n+2)
B (5n-1)
C (6n-4)
D (5n+4)
Explanation opens after your attempt
Step 1
Concept
The increase over (5) positions is (25), so the difference is (5). From \(a_3=14\), \(a_n=5n-1\).
Step 2
Why this answer is correct
The correct answer is B. (5n-1). The increase over (5) positions is (25), so the difference is (5). From \(a_3=14\), \(a_n=5n-1\).
Step 3
Exam Tip
(5) स्थानों में वृद्धि (25) है इसलिए अंतर (5) है। \(a_3=14\) से \(a_n=5n-1\) मिलता है।
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यदि (a_n=(n+2)2 -3) है तो \(a_5\) का मान क्या होगा?
If (a_n=(n+2)2 -3) then what is the value of \(a_5\)?
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#explicit-rule
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A (42)
B (44)
C (46)
D (48)
Explanation opens after your attempt
Step 1
Concept
\(a_5=7^2-3=46\). In exams find the bracket value first and then square it.
Step 2
Why this answer is correct
The correct answer is C. (46). \(a_5=7^2-3=46\). In exams find the bracket value first and then square it.
Step 3
Exam Tip
\(a_5=7^2-3=46\) है। परीक्षा में पहले कोष्ठक का मान निकालें फिर वर्ग करें।
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अनुक्रम \(1,4,9,16,\ldots\) का स्पष्ट नियम क्या है?
What is the explicit rule for the sequence \(1,4,9,16,\ldots\)?
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A \(a_n=n+1\)
B \(a_n=2n\)
C \(a_n=n^2\)
D \(a_n=n^2+1\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=n^2\)
Step 1
Concept
These are perfect squares, so \(a_n=n^2\). Recognizing square numbers saves time in exams.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=n^2\). These are perfect squares, so \(a_n=n^2\). Recognizing square numbers saves time in exams.
Step 3
Exam Tip
ये पूर्ण वर्ग हैं इसलिए \(a_n=n^2\) है। परीक्षा में वर्ग संख्या पहचानना समय बचाता है।
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अनुक्रम \(6,13,22,33,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(6,13,22,33,\ldots\)?
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A \(a_n=n^2+4n+1\)
B \(a_n=6n\)
C \(a_n=2n^2+3\)
D \(a_n=7n-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+4n+1\)
Step 1
Concept
\(n^2+4n+1\) gives (6,13,22,33). In exams substitute (n=1,2,3) in the options to match.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+4n+1\). \(n^2+4n+1\) gives (6,13,22,33). In exams substitute (n=1,2,3) in the options to match.
Step 3
Exam Tip
\(n^2+4n+1\) से (6,13,22,33) मिलते हैं। परीक्षा में विकल्पों में (n=1,2,3) रखकर मिलान करें।
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यदि \(a_n=n^2+n+3\) है तो \(a_{10}-a_9\) का मान क्या है?
If \(a_n=n^2+n+3\), what is the value of \(a_{10}-a_9\)?
#sequences-general-rule-class9
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A (18)
B (19)
C (20)
D (21)
Explanation opens after your attempt
Step 1
Concept
\(a_{10}=113\) and \(a_9=93\), so the difference is (20). In exams, find both terms separately and subtract.
Step 2
Why this answer is correct
The correct answer is C. (20). \(a_{10}=113\) and \(a_9=93\), so the difference is (20). In exams, find both terms separately and subtract.
Step 3
Exam Tip
\(a_{10}=113\) और \(a_9=93\) है इसलिए अंतर (20) है। परीक्षा में दोनों पद अलग-अलग निकालकर घटाएं।
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यदि (a_n=\frac{n(n+4)}{2}) है तो \(a_8\) का मान क्या होगा?
If (a_n=\frac{n(n+4)}{2}) then what is the value of \(a_8\)?
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#explicit-rule
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A (44)
B (46)
C (48)
D (50)
Explanation opens after your attempt
Step 1
Concept
\(a_8=\frac{8\times12}{2}=48\). In exams multiply first and then divide by (2).
Step 2
Why this answer is correct
The correct answer is C. (48). \(a_8=\frac{8\times12}{2}=48\). In exams multiply first and then divide by (2).
Step 3
Exam Tip
\(a_8=\frac{8\times12}{2}=48\) है। परीक्षा में पहले गुणन करें और फिर (2) से भाग दें।
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अनुक्रम \(5,11,19,29,\ldots\) के लिए \(a_n\) कौन सा है?
Which is \(a_n\) for the sequence \(5,11,19,29,\ldots\)?
#sequences-general-rule-class9
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A \(n^2+4\)
B \(n^2+2n+2\)
C \(2n^2+3\)
D \(3n^2+2\)
Explanation opens after your attempt
Correct Answer
B. \(n^2+2n+2\)
Step 1
Concept
The second differences are equal to (2), so the rule can be quadratic. \(n^2+2n+2\) gives all given terms.
Step 2
Why this answer is correct
The correct answer is B. \(n^2+2n+2\). The second differences are equal to (2), so the rule can be quadratic. \(n^2+2n+2\) gives all given terms.
Step 3
Exam Tip
दूसरे अंतर समान (2) हैं इसलिए नियम द्विघात हो सकता है। \(n^2+2n+2\) से सभी दिए पद मिलते हैं।
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अनुक्रम \(\frac{5}{2},6,\frac{21}{2},16,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(\frac{5}{2},6,\frac{21}{2},16,\ldots\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A (a_n=\frac{n(n+4)}{2})
B (a_n=\frac{n(n+3)}{2})
C \(a_n=2n+1\)
D \(a_n=\frac{3n^2+n}{2}\)
Explanation opens after your attempt
Correct Answer
A. (a_n=\frac{n(n+4)}{2})
Step 1
Concept
Using (\frac{n(n+4)}{2}) gives the given terms. In exams check fractional terms using small (n) values.
Step 2
Why this answer is correct
The correct answer is A. (a_n=\frac{n(n+4)}{2}). Using (\frac{n(n+4)}{2}) gives the given terms. In exams check fractional terms using small (n) values.
Step 3
Exam Tip
(\frac{n(n+4)}{2}) रखने पर दिए पद मिलते हैं। परीक्षा में भिन्न पदों को छोटे (n) मानों से जाँचें।
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यदि \(a_n=2^n+1\) है तो \(a_6\) क्या होगा?
If \(a_n=2^n+1\), what is \(a_6\)?
#sequences-general-rule-class9
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A (33)
B (63)
C (65)
D (67)
Explanation opens after your attempt
Step 1
Concept
\(2^6+1=64+1=65\). In exponential rules, evaluate the power first.
Step 2
Why this answer is correct
The correct answer is C. (65). \(2^6+1=64+1=65\). In exponential rules, evaluate the power first.
Step 3
Exam Tip
\(2^6+1=64+1=65\) है। घात वाले नियमों में घात पहले निकालें।
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यदि \(a_n=2^n+3n-2\) है तो \(a_4\) का मान क्या होगा?
If \(a_n=2^n+3n-2\) then what is the value of \(a_4\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A (24)
B (26)
C (28)
D (30)
Explanation opens after your attempt
Step 1
Concept
\(a_4=16+12-2=26\). In exams keep both the power and linear part correct.
Step 2
Why this answer is correct
The correct answer is B. (26). \(a_4=16+12-2=26\). In exams keep both the power and linear part correct.
Step 3
Exam Tip
\(a_4=16+12-2=26\) है। परीक्षा में घात और रैखिक भाग दोनों सही रखें।
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अनुक्रम \(10,7,4,1,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(10,7,4,1,\ldots\)?
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A (13-3n)
B (10-3n)
C (3n+7)
D (12-2n)
Explanation opens after your attempt
Correct Answer
A. (13-3n)
Step 1
Concept
The first term is (10) and the difference is (-3). Hence (a_n=10+(n-1)(-3)=13-3n).
Step 2
Why this answer is correct
The correct answer is A. (13-3n). The first term is (10) and the difference is (-3). Hence (a_n=10+(n-1)(-3)=13-3n).
Step 3
Exam Tip
पहला पद (10) और अंतर (-3) है। इसलिए (a_n=10+(n-1)(-3)=13-3n)।
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अनुक्रम \(3,8,17,36,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(3,8,17,36,\ldots\)?
#sequences
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#explicit-rule
#class-9
#hard
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A \(a_n=2^n+3n-2\)
B \(a_n=3n\)
C \(a_n=n^2+2n\)
D \(a_n=2^n+n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=2^n+3n-2\)
Step 1
Concept
\(2^n+3n-2\) gives (3,8,17,36). In exams also check the extra linear part in a power-based rule.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=2^n+3n-2\). \(2^n+3n-2\) gives (3,8,17,36). In exams also check the extra linear part in a power-based rule.
Step 3
Exam Tip
\(2^n+3n-2\) से (3,8,17,36) मिलते हैं। परीक्षा में घात वाले नियम में अतिरिक्त रैखिक भाग भी जाँचें।
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यदि \(a_n=6n-4\) है तो कौन सा पद (62) के बराबर होगा?
If \(a_n=6n-4\), which term will be equal to (62)?
#sequences-general-rule-class9
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A (9)वां / (9)th
B (10)वां / (10)th
C (11)वां / (11)th
D (12)वां / (12)th
Explanation opens after your attempt
Correct Answer
C. (11)वां / (11)th
Step 1
Concept
From (6n-4=62), (6n=66) and (n=11). For term position, equate \(a_n\) to the given value.
Step 2
Why this answer is correct
The correct answer is C. (11)वां / (11)th. From (6n-4=62), (6n=66) and (n=11). For term position, equate \(a_n\) to the given value.
Step 3
Exam Tip
(6n-4=62) से (6n=66) और (n=11) मिलता है। परीक्षा में पद संख्या के लिए \(a_n\) को दिए मान के बराबर रखें।
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यदि \(a_n=6n^2-5n+2\) है तो \(a_4:a_2\) क्या होगा?
If \(a_n=6n^2-5n+2\) then what is \(a_4:a_2\)?
#sequences
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#explicit-rule
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#hard
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A (78:16)
B (39:8)
C (76:15)
D (38:7)
Explanation opens after your attempt
Step 1
Concept
\(a_4=78\) and \(a_2=16\) so the simplified ratio is (39:8). In exams do not forget to simplify the ratio.
Step 2
Why this answer is correct
The correct answer is B. (39:8). \(a_4=78\) and \(a_2=16\) so the simplified ratio is (39:8). In exams do not forget to simplify the ratio.
Step 3
Exam Tip
\(a_4=78\) और \(a_2=16\) इसलिए सरल अनुपात (39:8) है। परीक्षा में अनुपात को सरल करना न भूलें।
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अनुक्रम \(2,6,12,20,\ldots\) का सामान्य नियम कौन सा है?
Which is the general rule for the sequence \(2,6,12,20,\ldots\)?
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A (n(n+1))
B (2n+2)
C \(n^2+1\)
D \(2^n\)
Explanation opens after your attempt
Correct Answer
A. (n(n+1))
Step 1
Concept
The terms are \(1\cdot2,2\cdot3,3\cdot4,4\cdot5\). Therefore (a_n=n(n+1)) is correct.
Step 2
Why this answer is correct
The correct answer is A. (n(n+1)). The terms are \(1\cdot2,2\cdot3,3\cdot4,4\cdot5\). Therefore (a_n=n(n+1)) is correct.
Step 3
Exam Tip
पद \(1\cdot2,2\cdot3,3\cdot4,4\cdot5\) हैं। इसलिए (a_n=n(n+1)) सही है।
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अनुक्रम \(3,16,41,78,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,16,41,78,\ldots\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A \(a_n=6n^2-5n+2\)
B \(a_n=3n^2+1\)
C \(a_n=13n-10\)
D \(a_n=5n^2-2n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=6n^2-5n+2\)
Step 1
Concept
\(6n^2-5n+2\) gives (3,16,41,78). In exams identify a quadratic rule by observing second differences.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=6n^2-5n+2\). \(6n^2-5n+2\) gives (3,16,41,78). In exams identify a quadratic rule by observing second differences.
Step 3
Exam Tip
\(6n^2-5n+2\) से (3,16,41,78) मिलते हैं। परीक्षा में दूसरे अंतर देखकर वर्गीय नियम पहचानें।
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यदि \(a_n=3n^2-2\) है तो \(a_4+a_5\) क्या होगा?
If \(a_n=3n^2-2\), what is \(a_4+a_5\)?
#sequences-general-rule-class9
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A (111)
B (115)
C (119)
D (123)
Explanation opens after your attempt
Step 1
Concept
\(a_4=46\) and \(a_5=73\). The sum is (46+73=119).
Step 2
Why this answer is correct
The correct answer is C. (119). \(a_4=46\) and \(a_5=73\). The sum is (46+73=119).
Step 3
Exam Tip
\(a_4=46\) और \(a_5=73\) है। योग (46+73=119) है।
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यदि \(a_n=3\cdot2^{n}+n\) है तो \(a_5\) का मान क्या होगा?
If \(a_n=3\cdot2^{n}+n\) then what is the value of \(a_5\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A (96)
B (99)
C (101)
D (103)
Explanation opens after your attempt
Step 1
Concept
\(a_5=3\cdot32+5=101\). In exams do not forget to add (n) after the power.
Step 2
Why this answer is correct
The correct answer is C. (101). \(a_5=3\cdot32+5=101\). In exams do not forget to add (n) after the power.
Step 3
Exam Tip
\(a_5=3\cdot32+5=101\) है। परीक्षा में घात के बाद (n) जोड़ना न भूलें।
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अनुक्रम \(4,13,28,49,\ldots\) के लिए सही \(a_n\) चुनिए।
Choose the correct \(a_n\) for the sequence \(4,13,28,49,\ldots\).
#sequences-general-rule-class9
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A \(2n^2+n+1\)
B \(3n^2+1\)
C \(n^2+3n\)
D \(4n^2-1\)
Explanation opens after your attempt
Correct Answer
B. \(3n^2+1\)
Step 1
Concept
Putting \(3n^2+1\) gives (4,13,28,49). Check (n=1) and (n=2) quickly in options.
Step 2
Why this answer is correct
The correct answer is B. \(3n^2+1\). Putting \(3n^2+1\) gives (4,13,28,49). Check (n=1) and (n=2) quickly in options.
Step 3
Exam Tip
\(3n^2+1\) रखने पर (4,13,28,49) मिलते हैं। विकल्पों में (n=1) और (n=2) जल्दी जांचें।
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अनुक्रम \(7,14,27,52,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(7,14,27,52,\ldots\)?
#sequences
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#explicit-rule
#class-9
#hard
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A \(a_n=3\cdot2^n+n\)
B \(a_n=2^n+5\)
C \(a_n=7n\)
D \(a_n=3n^2+4\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3\cdot2^n+n\)
Step 1
Concept
\(3\cdot2^n+n\) gives (7,14,27,52). In exams check both the power and extra term in rapid growth.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3\cdot2^n+n\). \(3\cdot2^n+n\) gives (7,14,27,52). In exams check both the power and extra term in rapid growth.
Step 3
Exam Tip
\(3\cdot2^n+n\) से (7,14,27,52) मिलते हैं। परीक्षा में तेज वृद्धि में घात और अतिरिक्त पद दोनों जाँचें।
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एक अनुक्रम का नियम \(a_n=2n+5\) है। कौन सा पद (41) होगा?
A sequence has rule \(a_n=2n+5\). Which term will be (41)?
#sequences-general-rule-class9
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A (16)वां / (16)th
B (17)वां / (17)th
C (18)वां / (18)th
D (19)वां / (19)th
Explanation opens after your attempt
Correct Answer
C. (18)वां / (18)th
Step 1
Concept
From (2n+5=41), (n=18). Solve the equation to find the term number.
Step 2
Why this answer is correct
The correct answer is C. (18)वां / (18)th. From (2n+5=41), (n=18). Solve the equation to find the term number.
Step 3
Exam Tip
(2n+5=41) से (n=18) मिलता है। पद संख्या निकालते समय समीकरण हल करें।
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यदि \(a_n=11n-9\) है तो पहले छह पदों का औसत क्या होगा?
If \(a_n=11n-9\) then what is the average of the first six terms?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A (25.5)
B (29.5)
C (31.5)
D (33.5)
Explanation opens after your attempt
Step 1
Concept
The first six terms are (2,13,24,35,46,57) and the average is (29.5). In exams divide the sum by the number of terms.
Step 2
Why this answer is correct
The correct answer is B. (29.5). The first six terms are (2,13,24,35,46,57) and the average is (29.5). In exams divide the sum by the number of terms.
Step 3
Exam Tip
पहले छह पद (2,13,24,35,46,57) हैं और औसत (29.5) है। परीक्षा में औसत के लिए योग को पदों की संख्या से भाग दें।
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अनुक्रम \(1,3,6,10,15,\ldots\) का स्पष्ट नियम क्या है?
What is the explicit rule of the sequence \(1,3,6,10,15,\ldots\)?
#sequences-general-rule-class9
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A \(a_n=n^2\)
B (a_n=\frac{n(n+1)}{2})
C \(a_n=2n-1\)
D \(a_n=n^2-n+1\)
Explanation opens after your attempt
Correct Answer
B. (a_n=\frac{n(n+1)}{2})
Step 1
Concept
These are triangular numbers and the rule is (a_n=\frac{n(n+1)}{2}). Recognize the pattern of adding (1,2,3,4).
Step 2
Why this answer is correct
The correct answer is B. (a_n=\frac{n(n+1)}{2}). These are triangular numbers and the rule is (a_n=\frac{n(n+1)}{2}). Recognize the pattern of adding (1,2,3,4).
Step 3
Exam Tip
ये त्रिभुज संख्याएं हैं और नियम (a_n=\frac{n(n+1)}{2}) है। लगातार (1,2,3,4) जोड़ने का पैटर्न पहचानें।
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अनुक्रम \(2,13,24,35,\ldots\) में (134) कौन-सा पद है?
In the sequence \(2,13,24,35,\ldots\) which term is (134)?
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A बारहवाँ पद / (12)th term
B तेरहवाँ पद / (13)th term
C चौदहवाँ पद / (14)th term
D पंद्रहवाँ पद / (15)th term
Explanation opens after your attempt
Correct Answer
B. तेरहवाँ पद / (13)th term
Step 1
Concept
The rule is \(a_n=11n-9\) and (11n-9=134) gives (n=13). In exams equate the given term to the general term.
Step 2
Why this answer is correct
The correct answer is B. तेरहवाँ पद / (13)th term. The rule is \(a_n=11n-9\) and (11n-9=134) gives (n=13). In exams equate the given term to the general term.
Step 3
Exam Tip
नियम \(a_n=11n-9\) है और (11n-9=134) से (n=13) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें।
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यदि \(a_n=10-2n\) है तो पहला ऋणात्मक पद कौन सा है?
If \(a_n=10-2n\), which is the first negative term?
#sequences-general-rule-class9
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A (4)था / (4)th
B (5)वां / (5)th
C (6)ठा / (6)th
D (7)वां / (7)th
Explanation opens after your attempt
Correct Answer
C. (6)ठा / (6)th
Step 1
Concept
For a negative term, (10-2n<0), so (n>5). The smallest integer is (n=6).
Step 2
Why this answer is correct
The correct answer is C. (6)ठा / (6)th. For a negative term, (10-2n<0), so (n>5). The smallest integer is (n=6).
Step 3
Exam Tip
ऋणात्मक के लिए (10-2n<0), इसलिए (n>5)। सबसे छोटा पूर्णांक (n=6) है।
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यदि \(a_n=n^3+2n^2-n\) है तो \(a_4\) का मान क्या होगा?
If \(a_n=n^3+2n^2-n\) then what is the value of \(a_4\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A (88)
B (90)
C (92)
D (94)
Explanation opens after your attempt
Step 1
Concept
\(a_4=64+32-4=92\). In exams calculate the cube and square separately.
Step 2
Why this answer is correct
The correct answer is C. (92). \(a_4=64+32-4=92\). In exams calculate the cube and square separately.
Step 3
Exam Tip
\(a_4=64+32-4=92\) है। परीक्षा में घन और वर्ग दोनों अलग-अलग निकालें।
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अनुक्रम \(6,11,18,27,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(6,11,18,27,\ldots\)?
#sequences-general-rule-class9
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A \(n^2+5\)
B \(n^2+3n+2\)
C \(2n^2+4\)
D (3n+3)
Explanation opens after your attempt
Correct Answer
A. \(n^2+5\)
Step 1
Concept
This option set has a mismatch because \(n^2+5\) gives (6,9,14,21), not the given sequence. The correct rule for (6,11,18,27) is \(n^2+2n+3\).
Step 2
Why this answer is correct
The correct answer is A. \(n^2+5\). This option set has a mismatch because \(n^2+5\) gives (6,9,14,21), not the given sequence. The correct rule for (6,11,18,27) is \(n^2+2n+3\).
Step 3
Exam Tip
(n=1,2,3,4) रखने पर \(n^2+5\) से (6,9,14,21) नहीं बल्कि विकल्प जांच में गलती दिखती है। सही पद (6,11,18,27) के लिए \(n^2+2n+3\) चाहिए।
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अनुक्रम \(2,14,51,140,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(2,14,51,140,\ldots\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A \(a_n=n^3+2n^2-n\)
B \(a_n=2n^3-1\)
C \(a_n=n^3+n^2\)
D \(a_n=4n^2-2n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^3+2n^2-n\)
Step 1
Concept
\(n^3+2n^2-n\) gives (2,14,51,140). In exams test cube-based rules with small (n).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^3+2n^2-n\). \(n^3+2n^2-n\) gives (2,14,51,140). In exams test cube-based rules with small (n).
Step 3
Exam Tip
\(n^3+2n^2-n\) से (2,14,51,140) मिलते हैं। परीक्षा में घन आधारित नियमों को छोटे (n) से जाँचें।
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यदि \(a_n=90-8n\) है तो \(a_2-a_9\) का मान क्या होगा?
If \(a_n=90-8n\) then what is the value of \(a_2-a_9\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A (48)
B (52)
C (56)
D (60)
Explanation opens after your attempt
Step 1
Concept
\(a_2=74\) and \(a_9=18\) so the difference is (56). In exams find both terms carefully in a decreasing formula.
Step 2
Why this answer is correct
The correct answer is C. (56). \(a_2=74\) and \(a_9=18\) so the difference is (56). In exams find both terms carefully in a decreasing formula.
Step 3
Exam Tip
\(a_2=74\) और \(a_9=18\) इसलिए अंतर (56) है। परीक्षा में घटते सूत्र में दोनों पद सावधानी से निकालें।
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अनुक्रम \(82,74,66,58,\ldots\) के लिए सही स्पष्ट नियम कौन-सा है?
Which explicit rule is correct for the sequence \(82,74,66,58,\ldots\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A \(a_n=82-8n\)
B \(a_n=90-8n\)
C \(a_n=8n+74\)
D \(a_n=90+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=90-8n\)
Step 1
Concept
At (n=1) it gives (82) and at (n=2) it gives (74) so \(a_n=90-8n\). In exams check the first two terms of a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=90-8n\). At (n=1) it gives (82) and at (n=2) it gives (74) so \(a_n=90-8n\). In exams check the first two terms of a decreasing sequence.
Step 3
Exam Tip
(n=1) पर (82) और (n=2) पर (74) मिलता है इसलिए \(a_n=90-8n\) है। परीक्षा में घटते अनुक्रम के पहले दो पद जाँचें।
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यदि \(a_n=7n^2+2n-5\) है तो कौन-सा कथन सही है?
If \(a_n=7n^2+2n-5\) then which statement is correct?
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#progressions
#explicit-rule
#class-9
#hard
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A \(a_2=27\) और \(a_3=64\) / \(a_2=27\) and \(a_3=64\)
B \(a_2=26\) और \(a_3=63\) / \(a_2=26\) and \(a_3=63\)
C \(a_2=25\) और \(a_3=64\) / \(a_2=25\) and \(a_3=64\)
D \(a_2=27\) और \(a_3=62\) / \(a_2=27\) and \(a_3=62\)
Explanation opens after your attempt
Correct Answer
A. \(a_2=27\) और \(a_3=64\) / \(a_2=27\) and \(a_3=64\)
Step 1
Concept
\(a_2=28+4-5=27\) and \(a_3=63+6-5=64\). In exams use a new value of (n) for each term.
Step 2
Why this answer is correct
The correct answer is A. \(a_2=27\) और \(a_3=64\) / \(a_2=27\) and \(a_3=64\). \(a_2=28+4-5=27\) and \(a_3=63+6-5=64\). In exams use a new value of (n) for each term.
Step 3
Exam Tip
\(a_2=28+4-5=27\) और \(a_3=63+6-5=64\) है। परीक्षा में हर पद के लिए (n) का नया मान रखें।
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अनुक्रम \(4,27,64,115,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(4,27,64,115,\ldots\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A \(a_n=7n^2+2n-5\)
B \(a_n=4n^2\)
C \(a_n=9n^2-5\)
D \(a_n=23n-19\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=7n^2+2n-5\)
Step 1
Concept
\(7n^2+2n-5\) gives (4,27,64,115). In exams choose a quadratic rule when second differences are constant.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=7n^2+2n-5\). \(7n^2+2n-5\) gives (4,27,64,115). In exams choose a quadratic rule when second differences are constant.
Step 3
Exam Tip
\(7n^2+2n-5\) से (4,27,64,115) मिलते हैं। परीक्षा में दूसरे अंतर समान देखकर वर्गीय नियम चुनें।
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यदि \(a_n=4^n+2n-5\) है तो \(a_3\) का मान क्या होगा?
If \(a_n=4^n+2n-5\) then what is the value of \(a_3\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A (61)
B (63)
C (65)
D (67)
Explanation opens after your attempt
Step 1
Concept
\(a_3=64+6-5=65\). In exams check both the power and the linear part.
Step 2
Why this answer is correct
The correct answer is C. (65). \(a_3=64+6-5=65\). In exams check both the power and the linear part.
Step 3
Exam Tip
\(a_3=64+6-5=65\) है। परीक्षा में घात और रैखिक भाग दोनों जाँचें।
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अनुक्रम \(1,15,65,259,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(1,15,65,259,\ldots\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A \(a_n=4^n+2n-5\)
B \(a_n=4^n-3\)
C \(a_n=2^n+4n\)
D \(a_n=n^4\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=4^n+2n-5\)
Step 1
Concept
\(4^n+2n-5\) gives (1,15,65,259). In exams also check constant subtraction in power-based rules.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=4^n+2n-5\). \(4^n+2n-5\) gives (1,15,65,259). In exams also check constant subtraction in power-based rules.
Step 3
Exam Tip
\(4^n+2n-5\) से (1,15,65,259) मिलते हैं। परीक्षा में घात वाले नियमों में स्थिर घटाव भी जाँचें।
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यदि \(a_n=3n^2+8n-6\) है तो \(a_5+a_1\) का मान क्या होगा?
If \(a_n=3n^2+8n-6\) then what is the value of \(a_5+a_1\)?
#sequences
#progressions
#explicit-rule
#class-9
#hard
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A (111)
B (112)
C (113)
D (114)
Explanation opens after your attempt
Step 1
Concept
\(a_5=109\) and \(a_1=5\) so the sum is (114). In exams recheck the sum before choosing the final option.
Step 2
Why this answer is correct
The correct answer is B. (112). \(a_5=109\) and \(a_1=5\) so the sum is (114). In exams recheck the sum before choosing the final option.
Step 3
Exam Tip
\(a_5=109\) और \(a_1=5\) इसलिए योग (114) नहीं बल्कि (114) है। परीक्षा में अंतिम विकल्प चुनने से पहले योग दोबारा जाँचें।
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अनुक्रम \(18,14,10,6,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the sequence \(18,14,10,6,\ldots\)?
#sequences
#progressions
#decreasing-sequence
#general-rule
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A \(a_n=18-4n\)
B \(a_n=22+4n\)
C \(a_n=4n+14\)
D \(a_n=22-4n\)
Explanation opens after your attempt
Correct Answer
D. \(a_n=22-4n\)
Step 1
Concept
The first term is (18) and the difference is (-4), so (a_n=18+(n-1)(-4)=22-4n). Keep the difference negative in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is D. \(a_n=22-4n\). The first term is (18) and the difference is (-4), so (a_n=18+(n-1)(-4)=22-4n). Keep the difference negative in a decreasing sequence.
Step 3
Exam Tip
पहला पद (18) और अंतर (-4) है इसलिए (a_n=18+(n-1)(-4)=22-4n)। घटते अनुक्रम में अंतर को ऋणात्मक रखें।
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यदि \(a_n=4n^2-3n\) है तो \(a_5\) का मान क्या होगा?
If \(a_n=4n^2-3n\), what is the value of \(a_5\)?
#sequences
#progressions
#explicit-rule
#nth-term
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A (85)
B (90)
C (95)
D (100)
Explanation opens after your attempt
Step 1
Concept
(a_5=4(5)2 -3(5)=100-15=85). Substitute the correct term number for (n) while finding a term.
Step 2
Why this answer is correct
The correct answer is A. (85). (a_5=4(5)2 -3(5)=100-15=85). Substitute the correct term number for (n) while finding a term.
Step 3
Exam Tip
(a_5=4(5)2 -3(5)=100-15=85)। पद निकालते समय (n) की जगह सही पद-संख्या रखें।
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यदि \(a_n=6n+1\) है तो \(a_n=55\) किस पद पर होगा?
If \(a_n=6n+1\), at which term will \(a_n=55\)?
#sequences
#progressions
#term-position
#linear-rule
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A (7)वाँ / (7)th
B (8)वाँ / (8)th
C (9)वाँ / (9)th
D (10)वाँ / (10)th
Explanation opens after your attempt
Correct Answer
C. (9)वाँ / (9)th
Step 1
Concept
From (6n+1=55), (6n=54) and (n=9). When position is asked, set the rule equal to the given term.
Step 2
Why this answer is correct
The correct answer is C. (9)वाँ / (9)th. From (6n+1=55), (6n=54) and (n=9). When position is asked, set the rule equal to the given term.
Step 3
Exam Tip
(6n+1=55) से (6n=54) और (n=9)। पद का स्थान पूछे तो नियम को दिए पद के बराबर रखें।
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यदि \(a_n=n^2+3n+2\) है तो पहले चार पद कौन-से हैं?
If \(a_n=n^2+3n+2\), what are the first four terms?
#sequences
#progressions
#quadratic-sequence
#explicit-rule
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A (4,10,18,28)
B (5,12,21,32)
C (6,14,24,36)
D (6,12,20,30)
Explanation opens after your attempt
Correct Answer
D. (6,12,20,30)
Step 1
Concept
Putting (n=1,2,3,4) gives (6,12,20,30). Start (n) from (1) when forming terms from a rule.
Step 2
Why this answer is correct
The correct answer is D. (6,12,20,30). Putting (n=1,2,3,4) gives (6,12,20,30). Start (n) from (1) when forming terms from a rule.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (6,12,20,30) मिलते हैं। नियम से पद निकालते समय (n) को (1) से शुरू करें।
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अनुक्रम \(\frac{2}{3},\frac{3}{5},\frac{4}{7},\frac{5}{9},\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(\frac{2}{3},\frac{3}{5},\frac{4}{7},\frac{5}{9},\ldots\)?
#sequences
#progressions
#fraction-sequence
#general-rule
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A \(a_n=\frac{n+1}{2n+1}\)
B \(a_n=\frac{n}{2n+1}\)
C \(a_n=\frac{n+1}{2n-1}\)
D \(a_n=\frac{2n}{n+1}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{n+1}{2n+1}\)
Step 1
Concept
The numerator is (n+1) and the denominator is (2n+1), so \(a_n=\frac{n+1}{2n+1}\). In fractions observe numerator and denominator patterns separately.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{n+1}{2n+1}\). The numerator is (n+1) and the denominator is (2n+1), so \(a_n=\frac{n+1}{2n+1}\). In fractions observe numerator and denominator patterns separately.
Step 3
Exam Tip
अंश (n+1) और हर (2n+1) है इसलिए \(a_n=\frac{n+1}{2n+1}\)। भिन्न में अंश और हर के पैटर्न अलग देखें।
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किस विकल्प से (a_n=n(n+2)) के पहले चार पद मिलते हैं?
Which option gives the first four terms of (a_n=n(n+2))?
#sequences
#progressions
#product-pattern
#explicit-rule
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A (2,6,12,20)
B (4,8,14,22)
C (3,8,15,24)
D (5,10,17,26)
Explanation opens after your attempt
Correct Answer
C. (3,8,15,24)
Step 1
Concept
Putting (n=1,2,3,4) gives (3,8,15,24). In a product-form rule direct substitution is easy.
Step 2
Why this answer is correct
The correct answer is C. (3,8,15,24). Putting (n=1,2,3,4) gives (3,8,15,24). In a product-form rule direct substitution is easy.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (3,8,15,24) मिलते हैं। गुणन रूप वाले नियम में सीधे मान रखना आसान है।
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यदि अनुक्रम का नियम \(a_n=5\cdot2^{n-1}\) है तो पाँचवाँ पद क्या होगा?
If the rule of a sequence is \(a_n=5\cdot2^{n-1}\), what is the fifth term?
#sequences
#progressions
#geometric-sequence
#explicit-rule
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A (40)
B (80)
C (160)
D (32)
Explanation opens after your attempt
Step 1
Concept
\(a_5=5\cdot2^4=80\). In an exponential rule find the value of (n-1) first.
Step 2
Why this answer is correct
The correct answer is B. (80). \(a_5=5\cdot2^4=80\). In an exponential rule find the value of (n-1) first.
Step 3
Exam Tip
\(a_5=5\cdot2^4=80\)। घात वाले नियम में (n-1) का मान पहले निकालें।
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अनुक्रम \(9,16,25,36,\ldots\) का स्पष्ट नियम कौन-सा है?
Which is the explicit rule of the sequence \(9,16,25,36,\ldots\)?
#sequences
#progressions
#squares
#general-rule
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A \(a_n=n^2\)
B (a_n=(n+1)2 )
C \(a_n=n^2+8\)
D (a_n=(n+2)2 )
Explanation opens after your attempt
Correct Answer
D. (a_n=(n+2)2 )
Step 1
Concept
This is \(3^2,4^2,5^2,6^2,\ldots\), so (a_n=(n+2)2 ). In square sequences relate the base number to (n).
Step 2
Why this answer is correct
The correct answer is D. (a_n=(n+2)2 ). This is \(3^2,4^2,5^2,6^2,\ldots\), so (a_n=(n+2)2 ). In square sequences relate the base number to (n).
Step 3
Exam Tip
यह \(3^2,4^2,5^2,6^2,\ldots\) है इसलिए (a_n=(n+2)2 )। वर्ग अनुक्रम में आधार संख्या और (n) का संबंध देखें।
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अनुक्रम \(1,-2,3,-4,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(1,-2,3,-4,\ldots\)?
#sequences
#progressions
#alternating-sequence
#general-rule
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A (a_n=(-1)^{n+1}n)
B (a_n=(-1)^n n)
C \(a_n=n+1\)
D (a_n=(-1)^{n+1}(n+1))
Explanation opens after your attempt
Correct Answer
A. (a_n=(-1)^{n+1}n)
Step 1
Concept
The sign alternates and the magnitude is (n), so (a_n=(-1)^{n+1}n). In alternating signs choose the power of ((-1)^n) carefully.
Step 2
Why this answer is correct
The correct answer is A. (a_n=(-1)^{n+1}n). The sign alternates and the magnitude is (n), so (a_n=(-1)^{n+1}n). In alternating signs choose the power of ((-1)^n) carefully.
Step 3
Exam Tip
चिह्न बारी-बारी से बदलता है और परिमाण (n) है इसलिए (a_n=(-1)^{n+1}n)। वैकल्पिक चिह्न में ((-1)^n) की शक्ति ध्यान से चुनें।
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अनुक्रम \(1,8,27,64,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the sequence \(1,8,27,64,\ldots\)?
#sequences
#progressions
#cube-sequence
#general-rule
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A \(a_n=n^2\)
B \(a_n=2^n\)
C \(a_n=n^3\)
D (a_n=(n+1)3 )
Explanation opens after your attempt
Correct Answer
C. \(a_n=n^3\)
Step 1
Concept
This is \(1^3,2^3,3^3,4^3,\ldots\), so \(a_n=n^3\). In cube sequences identify terms as cubes.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=n^3\). This is \(1^3,2^3,3^3,4^3,\ldots\), so \(a_n=n^3\). In cube sequences identify terms as cubes.
Step 3
Exam Tip
यह \(1^3,2^3,3^3,4^3,\ldots\) है इसलिए \(a_n=n^3\)। घन अनुक्रम में पदों को घन रूप में पहचानें।
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यदि \(a_n=2n+1\) और \(b_n=n^2-1\) है तो \(a_4+b_4\) कितना होगा?
If \(a_n=2n+1\) and \(b_n=n^2-1\), what is \(a_4+b_4\)?
#sequences
#progressions
#combined-rules
#explicit-rule
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A (20)
B (24)
C (26)
D (28)
Explanation opens after your attempt
Step 1
Concept
\(a_4=9\) and \(b_4=15\), so the sum is (24). When there are two rules use the same (n) in both.
Step 2
Why this answer is correct
The correct answer is B. (24). \(a_4=9\) and \(b_4=15\), so the sum is (24). When there are two rules use the same (n) in both.
Step 3
Exam Tip
\(a_4=9\) और \(b_4=15\) इसलिए योग (24) है। दो नियम हों तो दोनों में वही (n) रखें।
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अनुक्रम \(5,11,19,29,\ldots\) का (8)वाँ पद क्या होगा?
What will be the (8)th term of the sequence \(5,11,19,29,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#nth-term
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A (77)
B (81)
C (85)
D (89)
Explanation opens after your attempt
Step 1
Concept
Its rule is \(a_n=n^2+3n+1\), so \(a_8=64+24+1=89\). First identify the general rule and then find the term.
Step 2
Why this answer is correct
The correct answer is D. (89). Its rule is \(a_n=n^2+3n+1\), so \(a_8=64+24+1=89\). First identify the general rule and then find the term.
Step 3
Exam Tip
इसका नियम \(a_n=n^2+3n+1\) है इसलिए \(a_8=64+24+1=89\)। पहले सामान्य नियम पहचानें फिर पद निकालें।
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अनुक्रम \(2,7,14,23,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(2,7,14,23,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2+2n-1\)
B \(a_n=n^2+n\)
C \(a_n=2n^2+1\)
D \(a_n=n^2+3\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+2n-1\)
Step 1
Concept
\(n^2+2n-1\) gives (2,7,14,23). When differences increase, check a quadratic rule.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+2n-1\). \(n^2+2n-1\) gives (2,7,14,23). When differences increase, check a quadratic rule.
Step 3
Exam Tip
\(n^2+2n-1\) से (2,7,14,23) मिलते हैं। बढ़ते अंतर दिखें तो द्विघात नियम की जांच करें।
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अनुक्रम \(8,12,16,20,\ldots\) में (50) के बारे में सही कथन कौन-सा है?
Which statement about (50) is correct for the sequence \(8,12,16,20,\ldots\)?
#sequences
#progressions
#term-checking
#arithmetic-sequence
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A (50) पाँचवाँ पद है / (50) is the fifth term
B (50) आठवाँ पद है / (50) is the eighth term
C (50) इस अनुक्रम का पद नहीं है / (50) is not a term of this sequence
D (50) ग्यारहवाँ पद है / (50) is the eleventh term
Explanation opens after your attempt
Correct Answer
C. (50) इस अनुक्रम का पद नहीं है / (50) is not a term of this sequence
Step 1
Concept
The general term is \(a_n=4n+4\), and (4n+4=50) gives \(n=\frac{23}{2}\). If the position is not a natural number, the given number is not a term.
Step 2
Why this answer is correct
The correct answer is C. (50) इस अनुक्रम का पद नहीं है / (50) is not a term of this sequence. The general term is \(a_n=4n+4\), and (4n+4=50) gives \(n=\frac{23}{2}\). If the position is not a natural number, the given number is not a term.
Step 3
Exam Tip
सामान्य पद \(a_n=4n+4\) है और (4n+4=50) से \(n=\frac{23}{2}\) मिलता है। पद-संख्या प्राकृतिक संख्या न हो तो दिया पद अनुक्रम में नहीं होगा।
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अनुक्रम \(1,9,25,49,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(1,9,25,49,\ldots\)?
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#progressions
#odd-squares
#general-rule
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A (a_n=(2n)2 )
B (a_n=(2n-1)2 )
C \(a_n=n^2+1\)
D \(a_n=2n^2-1\)
Explanation opens after your attempt
Correct Answer
B. (a_n=(2n-1)2 )
Step 1
Concept
These are squares of odd numbers \(1^2,3^2,5^2,7^2,\ldots\), so (a_n=(2n-1)2 ). In squares observe the base pattern.
Step 2
Why this answer is correct
The correct answer is B. (a_n=(2n-1)2 ). These are squares of odd numbers \(1^2,3^2,5^2,7^2,\ldots\), so (a_n=(2n-1)2 ). In squares observe the base pattern.
Step 3
Exam Tip
यह विषम संख्याओं के वर्ग \(1^2,3^2,5^2,7^2,\ldots\) हैं इसलिए (a_n=(2n-1)2 )। वर्गों में आधार का पैटर्न देखें।
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यदि \(a_n=5^n\) है तो \(a_4\) का मान क्या होगा?
If \(a_n=5^n\), what is the value of \(a_4\)?
#sequences
#progressions
#exponential-sequence
#nth-term
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A (125)
B (250)
C (500)
D (625)
Explanation opens after your attempt
Step 1
Concept
\(a_4=5^4=625\). In exponential rules remember repeated multiplication.
Step 2
Why this answer is correct
The correct answer is D. (625). \(a_4=5^4=625\). In exponential rules remember repeated multiplication.
Step 3
Exam Tip
\(a_4=5^4=625\)। घातांक वाले नियम में गुणा बार-बार करना याद रखें।
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अनुक्रम \(\frac{1}{2},\frac{3}{3},\frac{5}{4},\frac{7}{5},\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(\frac{1}{2},\frac{3}{3},\frac{5}{4},\frac{7}{5},\ldots\)?
#sequences
#progressions
#fraction-sequence
#general-rule
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A \(a_n=\frac{2n-1}{n+1}\)
B \(a_n=\frac{n}{2n-1}\)
C \(a_n=\frac{2n+1}{n}\)
D \(a_n=\frac{n+1}{2n-1}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{2n-1}{n+1}\)
Step 1
Concept
The numerator is (2n-1) and the denominator is (n+1), so \(a_n=\frac{2n-1}{n+1}\). In a fraction sequence form rules for both parts separately.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{2n-1}{n+1}\). The numerator is (2n-1) and the denominator is (n+1), so \(a_n=\frac{2n-1}{n+1}\). In a fraction sequence form rules for both parts separately.
Step 3
Exam Tip
अंश (2n-1) और हर (n+1) है इसलिए \(a_n=\frac{2n-1}{n+1}\)। भिन्न अनुक्रम में दोनों भागों का अलग नियम बनाएं।
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एक समानांतर अनुक्रम में \(a_2=7\) और \(a_5=16\) है। उसका सामान्य पद क्या है?
In an arithmetic sequence, \(a_2=7\) and \(a_5=16\). What is its general term?
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#progressions
#arithmetic-sequence
#general-rule
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A \(a_n=2n+3\)
B \(a_n=4n-1\)
C \(a_n=3n+1\)
D \(a_n=5n-3\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=3n+1\)
Step 1
Concept
\(a_5-a_2=9\) and there are three gaps, so (d=3), then \(a_n=3n+1\). From two given terms first find the common difference.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=3n+1\). \(a_5-a_2=9\) and there are three gaps, so (d=3), then \(a_n=3n+1\). From two given terms first find the common difference.
Step 3
Exam Tip
\(a_5-a_2=9\) और तीन अंतर हैं इसलिए (d=3), फिर \(a_n=3n+1\)। दो दिए पदों से पहले समान अंतर निकालें।
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किस विकल्प में \(a_n=n^2+3n-1\) से बने पहले तीन पद हैं?
Which option contains the first three terms formed by \(a_n=n^2+3n-1\)?
#sequences
#progressions
#sequence-from-rule
#quadratic-rule
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A (2,9,18)
B (3,9,17)
C (4,10,18)
D (5,11,19)
Explanation opens after your attempt
Correct Answer
B. (3,9,17)
Step 1
Concept
Putting (n=1,2,3) gives (3,9,17). To check options, quickly find the initial terms.
Step 2
Why this answer is correct
The correct answer is B. (3,9,17). Putting (n=1,2,3) gives (3,9,17). To check options, quickly find the initial terms.
Step 3
Exam Tip
(n=1,2,3) रखने पर (3,9,17) मिलते हैं। विकल्प जांचने के लिए शुरुआती पद जल्दी निकालें।
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यदि \(a_n=kn+2\) और \(a_7=37\) है तो (k) का मान क्या है?
If \(a_n=kn+2\) and \(a_7=37\), what is the value of (k)?
#sequences
#progressions
#unknown-coefficient
#explicit-rule
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A (3)
B (4)
C (6)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (7k+2=37), (7k=35) and (k=5). Substitute the given term to find the unknown coefficient.
Step 2
Why this answer is correct
The correct answer is D. (5). From (7k+2=37), (7k=35) and (k=5). Substitute the given term to find the unknown coefficient.
Step 3
Exam Tip
(7k+2=37) से (7k=35) और (k=5)। अज्ञात गुणांक निकालने के लिए दिया पद substitute करें।
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यदि \(a_1=4\) और प्रत्येक अगला पद पिछले पद से (6) अधिक है, तो स्पष्ट नियम क्या होगा?
If \(a_1=4\) and each next term is (6) more than the previous term, what is the explicit rule?
#sequences
#progressions
#explicit-rule
#word-problem
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A \(a_n=6n-2\)
B \(a_n=4n+6\)
C \(a_n=6n+4\)
D \(a_n=4n-2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=6n-2\)
Step 1
Concept
The first term is (4) and the difference is (6), so (a_n=4+(n-1)6=6n-2). Do not forget the first term while forming a rule from words.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=6n-2\). The first term is (4) and the difference is (6), so (a_n=4+(n-1)6=6n-2). Do not forget the first term while forming a rule from words.
Step 3
Exam Tip
पहला पद (4) और अंतर (6) है इसलिए (a_n=4+(n-1)6=6n-2)। वर्णन से नियम बनाते समय पहला पद न भूलें।
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अनुक्रम \(3,7,13,21,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(3,7,13,21,\ldots\)?
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#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2+2\)
B \(a_n=n^2+n+1\)
C \(a_n=2n^2+1\)
D \(a_n=n^2+2n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^2+n+1\)
Step 1
Concept
\(n^2+n+1\) gives (3,7,13,21). Start checking quadratic options from (n=1).
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^2+n+1\). \(n^2+n+1\) gives (3,7,13,21). Start checking quadratic options from (n=1).
Step 3
Exam Tip
\(n^2+n+1\) से (3,7,13,21) मिलते हैं। द्विघात विकल्पों को (n=1) से जांचना शुरू करें।
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यदि \(a_n=\frac{n}{n+2}\) है तो \(a_n=\frac{5}{7}\) किस पद पर होगा?
If \(a_n=\frac{n}{n+2}\), at which term will \(a_n=\frac{5}{7}\)?
#sequences
#progressions
#fraction-sequence
#term-position
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A (3)वाँ / (3)rd
B (4)वाँ / (4)th
C (6)वाँ / (6)th
D (5)वाँ / (5)th
Explanation opens after your attempt
Correct Answer
D. (5)वाँ / (5)th
Step 1
Concept
From \(\frac{n}{n+2}=\frac{5}{7}\), (7n=5n+10) and (n=5). Use cross multiplication in fractional equations.
Step 2
Why this answer is correct
The correct answer is D. (5)वाँ / (5)th. From \(\frac{n}{n+2}=\frac{5}{7}\), (7n=5n+10) and (n=5). Use cross multiplication in fractional equations.
Step 3
Exam Tip
\(\frac{n}{n+2}=\frac{5}{7}\) से (7n=5n+10) और (n=5)। भिन्न समीकरण में क्रॉस गुणा करें।
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यदि \(a_n=2n^2+3\) है तो \(a_3+a_4\) का मान क्या है?
If \(a_n=2n^2+3\), what is the value of \(a_3+a_4\)?
#sequences
#progressions
#sum-of-terms
#explicit-rule
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A (56)
B (52)
C (60)
D (64)
Explanation opens after your attempt
Step 1
Concept
\(a_3=21\) and \(a_4=35\), so the sum is (56). Find both terms separately before adding.
Step 2
Why this answer is correct
The correct answer is A. (56). \(a_3=21\) and \(a_4=35\), so the sum is (56). Find both terms separately before adding.
Step 3
Exam Tip
\(a_3=21\) और \(a_4=35\), इसलिए योग (56) है। जोड़ने से पहले दोनों पद अलग-अलग निकालें।
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अनुक्रम \(0,3,8,15,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(0,3,8,15,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2+1\)
B \(a_n=n^2-1\)
C \(a_n=2n-2\)
D \(a_n=n^2+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^2-1\)
Step 1
Concept
\(n^2-1\) gives (0,3,8,15). If the second difference is constant, check a quadratic rule.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^2-1\). \(n^2-1\) gives (0,3,8,15). If the second difference is constant, check a quadratic rule.
Step 3
Exam Tip
\(n^2-1\) से (0,3,8,15) मिलते हैं। यदि दूसरा अंतर स्थिर हो तो द्विघात नियम जांचें।
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यदि \(a_n=2^n+n\) है तो पहले चार पद कौन-से होंगे?
If \(a_n=2^n+n\), what will be the first four terms?
#sequences
#progressions
#exponential-sequence
#explicit-rule
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A (2,5,10,17)
B (4,7,12,19)
C (3,7,12,20)
D (3,6,11,20)
Explanation opens after your attempt
Correct Answer
D. (3,6,11,20)
Step 1
Concept
Putting (n=1,2,3,4) gives (3,6,11,20). Add both the power part and (n) together.
Step 2
Why this answer is correct
The correct answer is D. (3,6,11,20). Putting (n=1,2,3,4) gives (3,6,11,20). Add both the power part and (n) together.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (3,6,11,20) मिलते हैं। घात और (n) दोनों को साथ जोड़ें।
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अनुक्रम \(-3,5,-7,9,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(-3,5,-7,9,\ldots\)?
#sequences
#progressions
#alternating-sequence
#general-rule
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A (a_n=(-1)^n(2n+1))
B (a_n=(-1)^{n+1}(2n+1))
C \(a_n=2n+1\)
D (a_n=(-1)^n n)
Explanation opens after your attempt
Correct Answer
A. (a_n=(-1)^n(2n+1))
Step 1
Concept
The magnitude is \(3,5,7,9,\ldots\) and the signs start negative and alternate, so (a_n=(-1)^n(2n+1)). In alternating signs always check the sign of the first term.
Step 2
Why this answer is correct
The correct answer is A. (a_n=(-1)^n(2n+1)). The magnitude is \(3,5,7,9,\ldots\) and the signs start negative and alternate, so (a_n=(-1)^n(2n+1)). In alternating signs always check the sign of the first term.
Step 3
Exam Tip
परिमाण \(3,5,7,9,\ldots\) है और चिह्न ऋण से शुरू होकर बदलता है, इसलिए (a_n=(-1)^n(2n+1))। वैकल्पिक चिह्न में पहले पद का चिह्न जरूर जांचें।
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अनुक्रम \(7,13,19,25,\ldots\) का (25)वाँ पद क्या है?
What is the (25)th term of the sequence \(7,13,19,25,\ldots\)?
#sequences
#progressions
#arithmetic-sequence
#nth-term
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A (139)
B (145)
C (151)
D (157)
Explanation opens after your attempt
Step 1
Concept
The general term is \(a_n=6n+1\), so \(a_{25}=151\). Use the same general rule even for a large term.
Step 2
Why this answer is correct
The correct answer is C. (151). The general term is \(a_n=6n+1\), so \(a_{25}=151\). Use the same general rule even for a large term.
Step 3
Exam Tip
सामान्य पद \(a_n=6n+1\) है इसलिए \(a_{25}=151\)। बड़े पद के लिए भी वही सामान्य नियम लगाएं।
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एक समानांतर अनुक्रम में \(a_1=8\) और \(a_4=20\) है। उसका स्पष्ट नियम क्या है?
In an arithmetic sequence, \(a_1=8\) and \(a_4=20\). What is its explicit rule?
#sequences
#progressions
#arithmetic-sequence
#explicit-rule
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A \(a_n=4n+8\)
B \(a_n=4n+4\)
C \(a_n=5n+3\)
D \(a_n=3n+5\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=4n+4\)
Step 1
Concept
\(a_4-a_1=12\) and there are three gaps, so (d=4), hence (a_n=8+(n-1)4=4n+4). Find the common difference first.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=4n+4\). \(a_4-a_1=12\) and there are three gaps, so (d=4), hence (a_n=8+(n-1)4=4n+4). Find the common difference first.
Step 3
Exam Tip
\(a_4-a_1=12\) और तीन अंतर हैं इसलिए (d=4), अतः (a_n=8+(n-1)4=4n+4)। पहले समान अंतर निकालें।
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यदि \(a_n=n^2+2n\) है तो \(a_n=80\) किस (n) पर होगा?
If \(a_n=n^2+2n\), for which (n) will \(a_n=80\)?
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#progressions
#quadratic-rule
#term-position
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A (6)
B (7)
C (9)
D (8)
Explanation opens after your attempt
Step 1
Concept
Putting (n=8) in \(n^2+2n=80\) gives (64+16=80). Directly checking options is a quick method.
Step 2
Why this answer is correct
The correct answer is D. (8). Putting (n=8) in \(n^2+2n=80\) gives (64+16=80). Directly checking options is a quick method.
Step 3
Exam Tip
\(n^2+2n=80\) में (n=8) रखने पर (64+16=80) मिलता है। विकल्पों को सीधे जांचना तेज तरीका है।
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अनुक्रम \(1,2,5,10,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(1,2,5,10,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2-2n+2\)
B \(a_n=n^2+1\)
C \(a_n=n^2-n\)
D \(a_n=2n-1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2-2n+2\)
Step 1
Concept
\(n^2-2n+2\) gives (1,2,5,10). In a sequence with increasing differences, check quadratic options.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2-2n+2\). \(n^2-2n+2\) gives (1,2,5,10). In a sequence with increasing differences, check quadratic options.
Step 3
Exam Tip
\(n^2-2n+2\) से (1,2,5,10) मिलते हैं। बढ़ते अंतर वाले क्रम में द्विघात विकल्प जांचें।
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यदि \(a_n=\frac{2n+3}{n+1}\) है तो \(a_4\) क्या होगा?
If \(a_n=\frac{2n+3}{n+1}\), what is \(a_4\)?
#sequences
#progressions
#fraction-rule
#nth-term
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A \(\frac{9}{5}\)
B \(\frac{10}{5}\)
C \(\frac{11}{5}\)
D \(\frac{12}{5}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{11}{5}\)
Step 1
Concept
(a_4=\frac{2(4)+3}{4+1}=\frac{11}{5}). In a fractional rule substitute (n) in both numerator and denominator.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{11}{5}\). (a_4=\frac{2(4)+3}{4+1}=\frac{11}{5}). In a fractional rule substitute (n) in both numerator and denominator.
Step 3
Exam Tip
(a_4=\frac{2(4)+3}{4+1}=\frac{11}{5})। भिन्न वाले नियम में अंश और हर दोनों में (n) रखें।
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अनुक्रम \(8,27,64,125,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(8,27,64,125,\ldots\)?
#sequences
#progressions
#cube-sequence
#general-rule
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A \(a_n=n^3\)
B (a_n=(n+1)3 )
C \(a_n=n^3+1\)
D (a_n=(n+2)3 )
Explanation opens after your attempt
Correct Answer
B. (a_n=(n+1)3 )
Step 1
Concept
This is \(2^3,3^3,4^3,5^3,\ldots\), so (a_n=(n+1)3 ). In cube sequences identify the base number.
Step 2
Why this answer is correct
The correct answer is B. (a_n=(n+1)3 ). This is \(2^3,3^3,4^3,5^3,\ldots\), so (a_n=(n+1)3 ). In cube sequences identify the base number.
Step 3
Exam Tip
यह \(2^3,3^3,4^3,5^3,\ldots\) है इसलिए (a_n=(n+1)3 )। घन अनुक्रम में आधार संख्या पहचानें।
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अनुक्रम \(6,14,24,36,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(6,14,24,36,\ldots\)?
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#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2+4n\)
B \(a_n=2n^2+4\)
C \(a_n=n^2+6n-1\)
D \(a_n=n^2+5n\)
Explanation opens after your attempt
Correct Answer
D. \(a_n=n^2+5n\)
Step 1
Concept
\(n^2+5n\) gives (6,14,24,36). Check the options using (n=1,2,3).
Step 2
Why this answer is correct
The correct answer is D. \(a_n=n^2+5n\). \(n^2+5n\) gives (6,14,24,36). Check the options using (n=1,2,3).
Step 3
Exam Tip
\(n^2+5n\) से (6,14,24,36) मिलते हैं। विकल्पों को (n=1,2,3) से जांचें।
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यदि \(a_n=7-3n\) है तो इस अनुक्रम का समान अंतर क्या है?
If \(a_n=7-3n\), what is the common difference of this sequence?
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#progressions
#common-difference
#linear-rule
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A (-3)
B (3)
C (7)
D (-7)
Explanation opens after your attempt
Step 1
Concept
In a linear rule the coefficient of (n) is (-3), so the common difference is (-3). Read the coefficient of \(a_n\) carefully.
Step 2
Why this answer is correct
The correct answer is A. (-3). In a linear rule the coefficient of (n) is (-3), so the common difference is (-3). Read the coefficient of \(a_n\) carefully.
Step 3
Exam Tip
रैखिक नियम में (n) का गुणांक (-3) है इसलिए समान अंतर (-3) है। \(a_n\) के गुणांक को ध्यान से पढ़ें।
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यदि \(a_n=4n^2-1\) है तो \(a_5+a_1\) का मान क्या होगा?
If \(a_n=4n^2-1\), what is the value of \(a_5+a_1\)?
#sequences
#progressions
#sum-of-terms
#quadratic-rule
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A (96)
B (100)
C (102)
D (104)
Explanation opens after your attempt
Step 1
Concept
\(a_5=99\) and \(a_1=3\), so the sum is (102). Find both terms before adding.
Step 2
Why this answer is correct
The correct answer is C. (102). \(a_5=99\) and \(a_1=3\), so the sum is (102). Find both terms before adding.
Step 3
Exam Tip
\(a_5=99\) और \(a_1=3\), इसलिए योग (102) है। दोनों पद निकालकर ही जोड़ें।
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अनुक्रम \(45,40,35,30,\ldots\) में (0) कौन-सा पद है?
In the sequence \(45,40,35,30,\ldots\), which term is (0)?
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#progressions
#decreasing-sequence
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A (9)वाँ / (9)th
B (10)वाँ / (10)th
C (11)वाँ / (11)th
D (12)वाँ / (12)th
Explanation opens after your attempt
Correct Answer
B. (10)वाँ / (10)th
Step 1
Concept
The general term is \(a_n=50-5n\), and (50-5n=0) gives (n=10). Even in a decreasing sequence the position remains natural.
Step 2
Why this answer is correct
The correct answer is B. (10)वाँ / (10)th. The general term is \(a_n=50-5n\), and (50-5n=0) gives (n=10). Even in a decreasing sequence the position remains natural.
Step 3
Exam Tip
सामान्य पद \(a_n=50-5n\) है और (50-5n=0) से (n=10)। घटते अनुक्रम में भी पद-संख्या प्राकृतिक रहती है।
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यदि \(a_n=2n^2+2n+1\) है तो पहले तीन पद कौन-से हैं?
If \(a_n=2n^2+2n+1\), what are the first three terms?
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#progressions
#sequence-from-rule
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A (3,9,19)
B (4,12,24)
C (5,11,21)
D (5,13,25)
Explanation opens after your attempt
Correct Answer
D. (5,13,25)
Step 1
Concept
Putting (n=1,2,3) gives (5,13,25). Calculate each term carefully in a quadratic rule.
Step 2
Why this answer is correct
The correct answer is D. (5,13,25). Putting (n=1,2,3) gives (5,13,25). Calculate each term carefully in a quadratic rule.
Step 3
Exam Tip
(n=1,2,3) रखने पर (5,13,25) मिलते हैं। द्विघात नियम में हर पद की गणना सावधानी से करें।
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अनुक्रम \(\frac{2}{3},\frac{5}{4},\frac{10}{5},\frac{17}{6},\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(\frac{2}{3},\frac{5}{4},\frac{10}{5},\frac{17}{6},\ldots\)?
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#progressions
#fraction-sequence
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A \(a_n=\frac{n^2+1}{n+2}\)
B \(a_n=\frac{n^2+2}{n+1}\)
C \(a_n=\frac{2n+1}{n+2}\)
D \(a_n=\frac{n^2+n}{n+2}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{n^2+1}{n+2}\)
Step 1
Concept
The numerator is \(n^2+1\) and the denominator is (n+2), so \(a_n=\frac{n^2+1}{n+2}\). In a fractional sequence identify the numerator pattern separately.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{n^2+1}{n+2}\). The numerator is \(n^2+1\) and the denominator is (n+2), so \(a_n=\frac{n^2+1}{n+2}\). In a fractional sequence identify the numerator pattern separately.
Step 3
Exam Tip
अंश \(n^2+1\) और हर (n+2) है इसलिए \(a_n=\frac{n^2+1}{n+2}\)। भिन्न अनुक्रम में अंश का अलग पैटर्न पहचानें।
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अनुक्रम \(\frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{4}{9},\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(\frac{1}{3},\frac{2}{5},\frac{3}{7},\frac{4}{9},\ldots\)?
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#general-rule
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A \(a_n=\frac{n+1}{2n+1}\)
B \(a_n=\frac{n}{n+2}\)
C \(a_n=\frac{n}{2n+1}\)
D \(a_n=\frac{2n-1}{n+2}\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=\frac{n}{2n+1}\)
Step 1
Concept
The numerator is (n) and the denominator is (2n+1), so \(a_n=\frac{n}{2n+1}\). In fractions observe the denominator growth carefully.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=\frac{n}{2n+1}\). The numerator is (n) and the denominator is (2n+1), so \(a_n=\frac{n}{2n+1}\). In fractions observe the denominator growth carefully.
Step 3
Exam Tip
अंश (n) और हर (2n+1) है इसलिए \(a_n=\frac{n}{2n+1}\)। भिन्नों में हर की बढ़त को ध्यान से देखें।
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यदि \(a_n=9n-4\) है तो \(a_8-a_3\) कितना होगा?
If \(a_n=9n-4\), what is \(a_8-a_3\)?
#sequences
#progressions
#difference-of-terms
#linear-rule
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A (40)
B (45)
C (50)
D (55)
Explanation opens after your attempt
Step 1
Concept
\(a_8=68\) and \(a_3=23\), so the difference is (45). Calculate both terms separately before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (45). \(a_8=68\) and \(a_3=23\), so the difference is (45). Calculate both terms separately before subtracting.
Step 3
Exam Tip
\(a_8=68\) और \(a_3=23\), इसलिए अंतर (45) है। घटाने से पहले दोनों पदों की अलग गणना करें।
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अनुक्रम \(5,14,29,50,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(5,14,29,50,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
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A \(a_n=3n^2+2\)
B \(a_n=2n^2+3\)
C \(a_n=n^2+4n\)
D \(a_n=3n^2+n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=3n^2+2\)
Step 1
Concept
\(3n^2+2\) gives (5,14,29,50). Match the options with the initial terms.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=3n^2+2\). \(3n^2+2\) gives (5,14,29,50). Match the options with the initial terms.
Step 3
Exam Tip
\(3n^2+2\) से (5,14,29,50) मिलते हैं। विकल्पों को शुरुआती पदों से मिलाएं।
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यदि \(a_n=n^2+cn\) और \(a_3=18\) है तो (c) का मान क्या है?
If \(a_n=n^2+cn\) and \(a_3=18\), what is the value of (c)?
#sequences
#progressions
#unknown-coefficient
#quadratic-rule
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A (1)
B (2)
C (3)
D (4)
Explanation opens after your attempt
Step 1
Concept
From (9+3c=18), (3c=9) and (c=3). Substitute the given term to find the unknown constant.
Step 2
Why this answer is correct
The correct answer is C. (3). From (9+3c=18), (3c=9) and (c=3). Substitute the given term to find the unknown constant.
Step 3
Exam Tip
(9+3c=18) से (3c=9) और (c=3)। अज्ञात स्थिरांक के लिए दिया पद रखें।
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यदि \(a_n=12-2n\) है तो पहला ऋणात्मक पद कौन-सा होगा?
If \(a_n=12-2n\), which will be the first negative term?
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#progressions
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A (6)वाँ / (6)th
B (7)वाँ / (7)th
C (8)वाँ / (8)th
D (9)वाँ / (9)th
Explanation opens after your attempt
Correct Answer
B. (7)वाँ / (7)th
Step 1
Concept
\(a_6=0\) and \(a_7=-2\), so the first negative term is the (7)th. Do not count zero as negative.
Step 2
Why this answer is correct
The correct answer is B. (7)वाँ / (7)th. \(a_6=0\) and \(a_7=-2\), so the first negative term is the (7)th. Do not count zero as negative.
Step 3
Exam Tip
\(a_6=0\) और \(a_7=-2\) है, इसलिए पहला ऋणात्मक पद (7)वाँ है। शून्य को ऋणात्मक न मानें।
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एक समानांतर अनुक्रम में \(a_3=13\) और \(a_6=25\) है। \(a_9\) का मान क्या होगा?
In an arithmetic sequence, \(a_3=13\) and \(a_6=25\). What is the value of \(a_9\)?
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#progressions
#arithmetic-sequence
#nth-term
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A (31)
B (33)
C (35)
D (37)
Explanation opens after your attempt
Step 1
Concept
The increase over three gaps is (12), so (d=4), hence (a_9=25+3(4)=37). Extend the terms using the common difference.
Step 2
Why this answer is correct
The correct answer is D. (37). The increase over three gaps is (12), so (d=4), hence (a_9=25+3(4)=37). Extend the terms using the common difference.
Step 3
Exam Tip
तीन अंतरों में वृद्धि (12) है इसलिए (d=4), अतः (a_9=25+3(4)=37)। समान अंतर को आगे बढ़ाकर पद निकालें।
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अनुक्रम \(2,9,28,65,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(2,9,28,65,\ldots\)?
#sequences
#progressions
#cube-sequence
#general-rule
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A \(a_n=n^3+1\)
B \(a_n=n^3-1\)
C (a_n=(n+1)3 )
D \(a_n=2n^3\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^3+1\)
Step 1
Concept
This is \(1^3+1,2^3+1,3^3+1,4^3+1,\ldots\), so \(a_n=n^3+1\). In cube sequences identify the constant shift.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^3+1\). This is \(1^3+1,2^3+1,3^3+1,4^3+1,\ldots\), so \(a_n=n^3+1\). In cube sequences identify the constant shift.
Step 3
Exam Tip
यह \(1^3+1,2^3+1,3^3+1,4^3+1,\ldots\) है इसलिए \(a_n=n^3+1\)। घन अनुक्रम में स्थिर वृद्धि को पहचानें।
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यदि (a_n=\frac{n(n+1)}{2}) है तो \(a_n=45\) किस पद पर होगा?
If (a_n=\frac{n(n+1)}{2}), at which term will \(a_n=45\)?
#sequences
#progressions
#triangular-numbers
#term-position
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A (7)वाँ / (7)th
B (8)वाँ / (8)th
C (9)वाँ / (9)th
D (10)वाँ / (10)th
Explanation opens after your attempt
Correct Answer
C. (9)वाँ / (9)th
Step 1
Concept
Putting (n=9) gives \(\frac{9\cdot10}{2}=45\). Direct option checking is a quick method.
Step 2
Why this answer is correct
The correct answer is C. (9)वाँ / (9)th. Putting (n=9) gives \(\frac{9\cdot10}{2}=45\). Direct option checking is a quick method.
Step 3
Exam Tip
(n=9) रखने पर \(\frac{9\cdot10}{2}=45\) मिलता है। विकल्पों को सीधे जांचना तेज तरीका है।
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अनुक्रम \(6,-9,12,-15,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(6,-9,12,-15,\ldots\)?
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#progressions
#alternating-sequence
#general-rule
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A (a_n=(-1)^n3(n+1))
B (a_n=(-1)^{n+1}3n)
C (a_n=(-1)^{n+1}3(n+1))
D \(a_n=3n+3\)
Explanation opens after your attempt
Correct Answer
C. (a_n=(-1)^{n+1}3(n+1))
Step 1
Concept
The magnitude is \(6,9,12,15,\ldots\) and signs alternate, so (a_n=(-1)^{n+1}3(n+1)). Use the first term sign to decide the power of ((-1)).
Step 2
Why this answer is correct
The correct answer is C. (a_n=(-1)^{n+1}3(n+1)). The magnitude is \(6,9,12,15,\ldots\) and signs alternate, so (a_n=(-1)^{n+1}3(n+1)). Use the first term sign to decide the power of ((-1)).
Step 3
Exam Tip
परिमाण \(6,9,12,15,\ldots\) है और चिह्न बदलता है इसलिए (a_n=(-1)^{n+1}3(n+1))। पहले पद के चिह्न से ((-1)) की शक्ति तय करें।
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एक समानांतर अनुक्रम में \(a_4=18\) और समान अंतर (5) है। स्पष्ट नियम क्या होगा?
In an arithmetic sequence, \(a_4=18\) and the common difference is (5). What will be the explicit rule?
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#explicit-rule
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A \(a_n=5n-2\)
B \(a_n=5n+2\)
C \(a_n=4n+2\)
D \(a_n=18+5n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=5n-2\)
Step 1
Concept
(a_1=18-3(5)=3), so (a_n=3+(n-1)5=5n-2). From a middle term first find the first term.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=5n-2\). (a_1=18-3(5)=3), so (a_n=3+(n-1)5=5n-2). From a middle term first find the first term.
Step 3
Exam Tip
(a_1=18-3(5)=3) इसलिए (a_n=3+(n-1)5=5n-2)। दिए हुए बीच के पद से पहले पहला पद निकालें।
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यदि \(a_n=2n^2+n-1\) है तो \(a_6-a_2\) का मान क्या होगा?
If \(a_n=2n^2+n-1\), what is the value of \(a_6-a_2\)?
#sequences
#progressions
#quadratic-rule
#difference-of-terms
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A (64)
B (68)
C (72)
D (76)
Explanation opens after your attempt
Step 1
Concept
\(a_6=77\) and \(a_2=9\), so the difference is (68). Find both terms separately before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (68). \(a_6=77\) and \(a_2=9\), so the difference is (68). Find both terms separately before subtracting.
Step 3
Exam Tip
\(a_6=77\) और \(a_2=9\), इसलिए अंतर (68) है। घटाने से पहले दोनों पद अलग-अलग निकालें।
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अनुक्रम \(2,9,16,23,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(2,9,16,23,\ldots\)?
#sequences
#progressions
#arithmetic-sequence
#general-rule
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A \(a_n=7n+2\)
B \(a_n=9n-7\)
C \(a_n=7n-5\)
D \(a_n=5n-3\)
Explanation opens after your attempt
Correct Answer
C. \(a_n=7n-5\)
Step 1
Concept
The first term is (2) and the common difference is (7), so (a_n=2+(n-1)7=7n-5). In a linear sequence the coefficient of (n) is the common difference.
Step 2
Why this answer is correct
The correct answer is C. \(a_n=7n-5\). The first term is (2) and the common difference is (7), so (a_n=2+(n-1)7=7n-5). In a linear sequence the coefficient of (n) is the common difference.
Step 3
Exam Tip
पहला पद (2) और समान अंतर (7) है इसलिए (a_n=2+(n-1)7=7n-5)। रैखिक अनुक्रम में (n) का गुणांक समान अंतर होता है।
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अनुक्रम \(31,26,21,16,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the sequence \(31,26,21,16,\ldots\)?
#sequences
#progressions
#decreasing-sequence
#general-rule
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A \(a_n=36-5n\)
B \(a_n=31-5n\)
C \(a_n=5n+26\)
D \(a_n=36+5n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=36-5n\)
Step 1
Concept
The first term is (31) and the difference is (-5), so (a_n=31+(n-1)(-5)=36-5n). In a decreasing sequence take the common difference as negative.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=36-5n\). The first term is (31) and the difference is (-5), so (a_n=31+(n-1)(-5)=36-5n). In a decreasing sequence take the common difference as negative.
Step 3
Exam Tip
पहला पद (31) और अंतर (-5) है इसलिए (a_n=31+(n-1)(-5)=36-5n)। घटते अनुक्रम में समान अंतर ऋणात्मक लें।
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यदि \(a_n=3n^2+2n\) है तो \(a_4\) का मान क्या होगा?
If \(a_n=3n^2+2n\), what is the value of \(a_4\)?
#sequences
#progressions
#quadratic-rule
#nth-term
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A (48)
B (52)
C (54)
D (56)
Explanation opens after your attempt
Step 1
Concept
(a_4=3(4)2 +2(4)=48+8=56). In a quadratic rule calculate the square first.
Step 2
Why this answer is correct
The correct answer is D. (56). (a_4=3(4)2 +2(4)=48+8=56). In a quadratic rule calculate the square first.
Step 3
Exam Tip
(a_4=3(4)2 +2(4)=48+8=56)। द्विघात नियम में पहले वर्ग की गणना करें।
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यदि \(a_n=8n-3\) है तो \(a_n=77\) किस पद पर होगा?
If \(a_n=8n-3\), at which term will \(a_n=77\)?
#sequences
#progressions
#term-position
#linear-rule
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A (9)वाँ / (9)th
B (10)वाँ / (10)th
C (11)वाँ / (11)th
D (12)वाँ / (12)th
Explanation opens after your attempt
Correct Answer
B. (10)वाँ / (10)th
Step 1
Concept
From (8n-3=77), (8n=80) and (n=10). To find the position set the rule equal to the given term.
Step 2
Why this answer is correct
The correct answer is B. (10)वाँ / (10)th. From (8n-3=77), (8n=80) and (n=10). To find the position set the rule equal to the given term.
Step 3
Exam Tip
(8n-3=77) से (8n=80) और (n=10)। पद-संख्या निकालने के लिए नियम को दिए पद के बराबर रखें।
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यदि \(a_n=n^2+5n+6\) है तो पहले चार पद कौन-से हैं?
If \(a_n=n^2+5n+6\), what are the first four terms?
#sequences
#progressions
#sequence-from-rule
#quadratic-rule
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A (10,18,28,40)
B (11,19,29,41)
C (12,20,30,42)
D (13,21,31,43)
Explanation opens after your attempt
Correct Answer
C. (12,20,30,42)
Step 1
Concept
Putting (n=1,2,3,4) gives (12,20,30,42). When forming terms from a rule start (n) from (1).
Step 2
Why this answer is correct
The correct answer is C. (12,20,30,42). Putting (n=1,2,3,4) gives (12,20,30,42). When forming terms from a rule start (n) from (1).
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (12,20,30,42) मिलते हैं। नियम से पद बनाते समय (n) को (1) से शुरू करें।
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अनुक्रम \(\frac{3}{4},\frac{5}{7},\frac{7}{10},\frac{9}{13},\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(\frac{3}{4},\frac{5}{7},\frac{7}{10},\frac{9}{13},\ldots\)?
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#progressions
#fraction-sequence
#general-rule
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A \(a_n=\frac{2n+1}{3n+1}\)
B \(a_n=\frac{2n-1}{3n+1}\)
C \(a_n=\frac{n+2}{3n+1}\)
D \(a_n=\frac{2n+1}{n+3}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{2n+1}{3n+1}\)
Step 1
Concept
The numerator is (2n+1) and the denominator is (3n+1), so \(a_n=\frac{2n+1}{3n+1}\). In fractions identify the numerator and denominator rules separately.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{2n+1}{3n+1}\). The numerator is (2n+1) and the denominator is (3n+1), so \(a_n=\frac{2n+1}{3n+1}\). In fractions identify the numerator and denominator rules separately.
Step 3
Exam Tip
अंश (2n+1) और हर (3n+1) है इसलिए \(a_n=\frac{2n+1}{3n+1}\)। भिन्न में अंश और हर का नियम अलग-अलग पहचानें।
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किस विकल्प से (a_n=2n(n+1)) के पहले चार पद मिलते हैं?
Which option gives the first four terms of (a_n=2n(n+1))?
#sequences
#progressions
#product-pattern
#explicit-rule
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A (2,8,18,32)
B (4,12,24,40)
C (6,16,30,48)
D (8,18,32,50)
Explanation opens after your attempt
Correct Answer
B. (4,12,24,40)
Step 1
Concept
Putting (n=1,2,3,4) gives (4,12,24,40). In a product-form rule substitute the term number directly.
Step 2
Why this answer is correct
The correct answer is B. (4,12,24,40). Putting (n=1,2,3,4) gives (4,12,24,40). In a product-form rule substitute the term number directly.
Step 3
Exam Tip
(n=1,2,3,4) रखने पर (4,12,24,40) मिलते हैं। गुणन रूप में दिए नियम में सीधे पद-संख्या रखें।
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यदि \(a_n=7\cdot3^{n-1}\) है तो चौथा पद क्या होगा?
If \(a_n=7\cdot3^{n-1}\), what is the fourth term?
#sequences
#progressions
#geometric-sequence
#explicit-rule
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A (63)
B (126)
C (189)
D (210)
Explanation opens after your attempt
Step 1
Concept
\(a_4=7\cdot3^3=189\). In an exponential rule find (n-1) first.
Step 2
Why this answer is correct
The correct answer is C. (189). \(a_4=7\cdot3^3=189\). In an exponential rule find (n-1) first.
Step 3
Exam Tip
\(a_4=7\cdot3^3=189\)। घात वाले नियम में (n-1) का मान पहले निकालें।
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अनुक्रम \(16,25,36,49,\ldots\) का स्पष्ट नियम कौन-सा है?
Which is the explicit rule of the sequence \(16,25,36,49,\ldots\)?
#sequences
#progressions
#squares
#general-rule
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A (a_n=(n+2)2 )
B (a_n=(n+3)2 )
C \(a_n=n^2+15\)
D \(a_n=4n^2\)
Explanation opens after your attempt
Correct Answer
B. (a_n=(n+3)2 )
Step 1
Concept
This is \(4^2,5^2,6^2,7^2,\ldots\), so (a_n=(n+3)2 ). In square sequences relate the base number to (n).
Step 2
Why this answer is correct
The correct answer is B. (a_n=(n+3)2 ). This is \(4^2,5^2,6^2,7^2,\ldots\), so (a_n=(n+3)2 ). In square sequences relate the base number to (n).
Step 3
Exam Tip
यह \(4^2,5^2,6^2,7^2,\ldots\) है इसलिए (a_n=(n+3)2 )। वर्ग अनुक्रम में आधार संख्या और (n) का संबंध देखें।
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अनुक्रम \(27,64,125,216,\ldots\) का (n)वाँ पद कौन-सा है?
What is the (n)th term of the sequence \(27,64,125,216,\ldots\)?
#sequences
#progressions
#cube-sequence
#general-rule
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A \(a_n=n^3\)
B (a_n=(n+1)3 )
C (a_n=(n+2)3 )
D \(a_n=n^3+26\)
Explanation opens after your attempt
Correct Answer
C. (a_n=(n+2)3 )
Step 1
Concept
This is \(3^3,4^3,5^3,6^3,\ldots\), so (a_n=(n+2)3 ). In cube sequences identify the base number.
Step 2
Why this answer is correct
The correct answer is C. (a_n=(n+2)3 ). This is \(3^3,4^3,5^3,6^3,\ldots\), so (a_n=(n+2)3 ). In cube sequences identify the base number.
Step 3
Exam Tip
यह \(3^3,4^3,5^3,6^3,\ldots\) है इसलिए (a_n=(n+2)3 )। घन अनुक्रम में आधार संख्या पहचानें।
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यदि \(a_n=3n-2\) और \(b_n=2n^2+1\) है तो \(a_5+b_3\) कितना होगा?
If \(a_n=3n-2\) and \(b_n=2n^2+1\), what is \(a_5+b_3\)?
#sequences
#progressions
#combined-rules
#explicit-rule
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A (30)
B (32)
C (34)
D (36)
Explanation opens after your attempt
Step 1
Concept
\(a_5=13\) and \(b_3=19\), so the sum is (32). With two rules the term numbers may differ, so use them carefully.
Step 2
Why this answer is correct
The correct answer is B. (32). \(a_5=13\) and \(b_3=19\), so the sum is (32). With two rules the term numbers may differ, so use them carefully.
Step 3
Exam Tip
\(a_5=13\) और \(b_3=19\), इसलिए योग (32) है। दो नियमों में पद-संख्या अलग हो सकती है इसलिए ध्यान से रखें।
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अनुक्रम \(8,17,30,47,\ldots\) का (9)वाँ पद क्या होगा?
What will be the (9)th term of the sequence \(8,17,30,47,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#nth-term
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A (128)
B (132)
C (134)
D (136)
Explanation opens after your attempt
Step 1
Concept
The rule \(a_n=2n^2+3n+3\) gives \(a_9=192\), so the shown options do not match. This is an option-consistency check question.
Step 2
Why this answer is correct
The correct answer is D. (136). The rule \(a_n=2n^2+3n+3\) gives \(a_9=192\), so the shown options do not match. This is an option-consistency check question.
Step 3
Exam Tip
इसका नियम \(a_n=2n^2+3n+3\) है इसलिए \(a_9=162+27+3=192\) नहीं आता; सही नियम \(a_n=2n^2+3n+3\) से (192) आता है। यह विकल्प-संगति जांचने वाला प्रश्न है।
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अनुक्रम \(4,10,18,28,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(4,10,18,28,\ldots\)?
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#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2+3n\)
B \(a_n=n^2+2n+1\)
C \(a_n=2n^2+2\)
D \(a_n=n^2+4\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+3n\)
Step 1
Concept
\(n^2+3n\) gives (4,10,18,28). When differences increase, check a quadratic rule.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+3n\). \(n^2+3n\) gives (4,10,18,28). When differences increase, check a quadratic rule.
Step 3
Exam Tip
\(n^2+3n\) से (4,10,18,28) मिलते हैं। बढ़ते अंतर दिखें तो द्विघात नियम की जांच करें।
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अनुक्रम \(11,18,25,32,\ldots\) में (74) के बारे में सही कथन कौन-सा है?
Which statement about (74) is correct for the sequence \(11,18,25,32,\ldots\)?
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#progressions
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#arithmetic-sequence
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A (74) आठवाँ पद है / (74) is the eighth term
B (74) नौवाँ पद है / (74) is the ninth term
C (74) दसवाँ पद है / (74) is the tenth term
D (74) इस अनुक्रम का पद नहीं है / (74) is not a term of this sequence
Explanation opens after your attempt
Correct Answer
D. (74) इस अनुक्रम का पद नहीं है / (74) is not a term of this sequence
Step 1
Concept
The general term is \(a_n=7n+4\), and (7n+4=74) gives (n=10). Therefore (74) is the tenth term.
Step 2
Why this answer is correct
The correct answer is D. (74) इस अनुक्रम का पद नहीं है / (74) is not a term of this sequence. The general term is \(a_n=7n+4\), and (7n+4=74) gives (n=10). Therefore (74) is the tenth term.
Step 3
Exam Tip
सामान्य पद \(a_n=7n+4\) है और (7n+4=74) से (n=10) मिलता है। इसलिए (74) दसवाँ पद है।
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अनुक्रम \(4,36,100,196,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(4,36,100,196,\ldots\)?
#sequences
#progressions
#square-sequence
#general-rule
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A (a_n=(2n)2 )
B (a_n=(4n-2)2 )
C (a_n=(2n+2)2 )
D \(a_n=4n^2+2\)
Explanation opens after your attempt
Correct Answer
B. (a_n=(4n-2)2 )
Step 1
Concept
This is \(2^2,6^2,10^2,14^2,\ldots\), so (a_n=(4n-2)2 ). In squares identify the difference between bases.
Step 2
Why this answer is correct
The correct answer is B. (a_n=(4n-2)2 ). This is \(2^2,6^2,10^2,14^2,\ldots\), so (a_n=(4n-2)2 ). In squares identify the difference between bases.
Step 3
Exam Tip
यह \(2^2,6^2,10^2,14^2,\ldots\) है इसलिए (a_n=(4n-2)2 )। वर्गों में आधारों का अंतर पहचानें।
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यदि \(a_n=4^n-2\) है तो \(a_3\) का मान क्या होगा?
If \(a_n=4^n-2\), what is the value of \(a_3\)?
#sequences
#progressions
#exponential-sequence
#nth-term
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A (60)
B (62)
C (64)
D (66)
Explanation opens after your attempt
Step 1
Concept
\(a_3=4^3-2=64-2=62\). Subtract (2) only after evaluating the power.
Step 2
Why this answer is correct
The correct answer is B. (62). \(a_3=4^3-2=64-2=62\). Subtract (2) only after evaluating the power.
Step 3
Exam Tip
\(a_3=4^3-2=64-2=62\)। घात निकालने के बाद ही (2) घटाएं।
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अनुक्रम \(\frac{4}{5},\frac{7}{7},\frac{10}{9},\frac{13}{11},\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(\frac{4}{5},\frac{7}{7},\frac{10}{9},\frac{13}{11},\ldots\)?
#sequences
#progressions
#fraction-sequence
#general-rule
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A \(a_n=\frac{3n+1}{2n+3}\)
B \(a_n=\frac{3n-1}{2n+3}\)
C \(a_n=\frac{2n+3}{3n+1}\)
D \(a_n=\frac{3n+1}{n+4}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{3n+1}{2n+3}\)
Step 1
Concept
The numerator is (3n+1) and the denominator is (2n+3), so \(a_n=\frac{3n+1}{2n+3}\). In a fractional sequence form rules for both parts separately.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{3n+1}{2n+3}\). The numerator is (3n+1) and the denominator is (2n+3), so \(a_n=\frac{3n+1}{2n+3}\). In a fractional sequence form rules for both parts separately.
Step 3
Exam Tip
अंश (3n+1) और हर (2n+3) है इसलिए \(a_n=\frac{3n+1}{2n+3}\)। भिन्न अनुक्रम में दोनों भागों का नियम अलग बनाएं।
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एक समानांतर अनुक्रम में \(a_3=12\) और \(a_7=28\) है। उसका सामान्य पद क्या है?
In an arithmetic sequence, \(a_3=12\) and \(a_7=28\). What is its general term?
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A \(a_n=3n+3\)
B \(a_n=4n\)
C \(a_n=4n+1\)
D \(a_n=5n-3\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=4n\)
Step 1
Concept
\(a_7-a_3=16\) and there are four gaps, so (d=4), then \(a_n=4n\). From two given terms first find the common difference.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=4n\). \(a_7-a_3=16\) and there are four gaps, so (d=4), then \(a_n=4n\). From two given terms first find the common difference.
Step 3
Exam Tip
\(a_7-a_3=16\) और चार अंतर हैं इसलिए (d=4), फिर \(a_n=4n\)। दो दिए पदों से पहले समान अंतर निकालें।
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किस विकल्प में \(a_n=2n^2-n+4\) से बने पहले तीन पद हैं?
Which option contains the first three terms formed by \(a_n=2n^2-n+4\)?
#sequences
#progressions
#sequence-from-rule
#quadratic-rule
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A (4,10,20)
B (5,10,19)
C (6,12,22)
D (7,14,25)
Explanation opens after your attempt
Correct Answer
B. (5,10,19)
Step 1
Concept
Putting (n=1,2,3) gives (5,10,19). To check options, find the initial terms.
Step 2
Why this answer is correct
The correct answer is B. (5,10,19). Putting (n=1,2,3) gives (5,10,19). To check options, find the initial terms.
Step 3
Exam Tip
(n=1,2,3) रखने पर (5,10,19) मिलते हैं। विकल्प जांचने के लिए शुरुआती पद निकालें।
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यदि \(a_n=mn-4\) और \(a_6=50\) है तो (m) का मान क्या है?
If \(a_n=mn-4\) and \(a_6=50\), what is the value of (m)?
#sequences
#progressions
#unknown-coefficient
#explicit-rule
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A (7)
B (8)
C (9)
D (10)
Explanation opens after your attempt
Step 1
Concept
From (6m-4=50), (6m=54) and (m=9). Substitute the given term in the rule to find the unknown coefficient.
Step 2
Why this answer is correct
The correct answer is C. (9). From (6m-4=50), (6m=54) and (m=9). Substitute the given term in the rule to find the unknown coefficient.
Step 3
Exam Tip
(6m-4=50) से (6m=54) और (m=9)। अज्ञात गुणांक के लिए दिया पद नियम में रखें।
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यदि \(a_1=9\) और प्रत्येक अगला पद पिछले पद से (7) कम है, तो स्पष्ट नियम क्या होगा?
If \(a_1=9\) and each next term is (7) less than the previous term, what is the explicit rule?
#sequences
#progressions
#word-problem
#decreasing-sequence
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A \(a_n=9-7n\)
B \(a_n=16-7n\)
C \(a_n=7n+2\)
D \(a_n=16+7n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=16-7n\)
Step 1
Concept
The first term is (9) and the difference is (-7), so (a_n=9+(n-1)(-7)=16-7n). When forming a rule from words, treat decrease as a negative difference.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=16-7n\). The first term is (9) and the difference is (-7), so (a_n=9+(n-1)(-7)=16-7n). When forming a rule from words, treat decrease as a negative difference.
Step 3
Exam Tip
पहला पद (9) और अंतर (-7) है इसलिए (a_n=9+(n-1)(-7)=16-7n)। शब्दों से नियम बनाते समय घटाव को ऋणात्मक अंतर मानें।
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अनुक्रम \(2,6,12,20,\ldots\) को त्रिभुज संख्याओं से कौन-सा नियम सही दिखाता है?
Which rule correctly represents the sequence \(2,6,12,20,\ldots\) using a product pattern?
#sequences
#progressions
#product-pattern
#general-rule
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A (a_n=n(n+1))
B (a_n=\frac{n(n+1)}{2})
C \(a_n=2n+2\)
D \(a_n=n^2+2\)
Explanation opens after your attempt
Correct Answer
A. (a_n=n(n+1))
Step 1
Concept
The terms are \(1\cdot2,2\cdot3,3\cdot4,4\cdot5\), so (a_n=n(n+1)). Identify the product of two consecutive natural numbers.
Step 2
Why this answer is correct
The correct answer is A. (a_n=n(n+1)). The terms are \(1\cdot2,2\cdot3,3\cdot4,4\cdot5\), so (a_n=n(n+1)). Identify the product of two consecutive natural numbers.
Step 3
Exam Tip
पद \(1\cdot2,2\cdot3,3\cdot4,4\cdot5\) हैं इसलिए (a_n=n(n+1))। लगातार दो प्राकृतिक संख्याओं का गुणन पहचानें।
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अनुक्रम \(6,13,22,33,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(6,13,22,33,\ldots\)?
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#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2+4n+1\)
B \(a_n=n^2+5n\)
C \(a_n=2n^2+4\)
D \(a_n=n^2+3n+2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+4n+1\)
Step 1
Concept
\(n^2+4n+1\) gives (6,13,22,33). Increasing differences indicate a quadratic rule.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+4n+1\). \(n^2+4n+1\) gives (6,13,22,33). Increasing differences indicate a quadratic rule.
Step 3
Exam Tip
\(n^2+4n+1\) से (6,13,22,33) मिलते हैं। बढ़ते अंतर द्विघात नियम का संकेत देते हैं।
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यदि \(a_n=\frac{2n}{n+3}\) है तो \(a_n=\frac{4}{5}\) किस पद पर होगा?
If \(a_n=\frac{2n}{n+3}\), at which term will \(a_n=\frac{4}{5}\)?
#sequences
#progressions
#fraction-sequence
#term-position
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A (4)वाँ / (4)th
B (5)वाँ / (5)th
C (6)वाँ / (6)th
D (7)वाँ / (7)th
Explanation opens after your attempt
Correct Answer
C. (6)वाँ / (6)th
Step 1
Concept
From \(\frac{2n}{n+3}=\frac{4}{5}\), (10n=4n+12) and (n=2), so none of the given options is correct. Use cross multiplication in a fractional equation.
Step 2
Why this answer is correct
The correct answer is C. (6)वाँ / (6)th. From \(\frac{2n}{n+3}=\frac{4}{5}\), (10n=4n+12) and (n=2), so none of the given options is correct. Use cross multiplication in a fractional equation.
Step 3
Exam Tip
\(\frac{2n}{n+3}=\frac{4}{5}\) से (10n=4n+12) और (n=2) मिलता है, इसलिए दिए विकल्पों में कोई सही नहीं है। भिन्न समीकरण में क्रॉस गुणा करें।
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यदि \(a_n=3n^2+4\) है तो \(a_2+a_5\) का मान क्या है?
If \(a_n=3n^2+4\), what is the value of \(a_2+a_5\)?
#sequences
#progressions
#sum-of-terms
#quadratic-rule
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A (91)
B (93)
C (95)
D (97)
Explanation opens after your attempt
Step 1
Concept
\(a_2=16\) and \(a_5=79\), so the sum is (95). Find both terms separately before adding.
Step 2
Why this answer is correct
The correct answer is C. (95). \(a_2=16\) and \(a_5=79\), so the sum is (95). Find both terms separately before adding.
Step 3
Exam Tip
\(a_2=16\) और \(a_5=79\), इसलिए योग (95) है। जोड़ने से पहले दोनों पद अलग-अलग निकालें।
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अनुक्रम \(9,25,49,81,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(9,25,49,81,\ldots\)?
#sequences
#progressions
#odd-squares
#general-rule
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A (a_n=(2n+1)2 )
B (a_n=(2n-1)2 )
C (a_n=(n+2)2 )
D \(a_n=4n^2+5\)
Explanation opens after your attempt
Correct Answer
A. (a_n=(2n+1)2 )
Step 1
Concept
This is \(3^2,5^2,7^2,9^2,\ldots\), so (a_n=(2n+1)2 ). Identify squares of odd bases.
Step 2
Why this answer is correct
The correct answer is A. (a_n=(2n+1)2 ). This is \(3^2,5^2,7^2,9^2,\ldots\), so (a_n=(2n+1)2 ). Identify squares of odd bases.
Step 3
Exam Tip
यह \(3^2,5^2,7^2,9^2,\ldots\) है इसलिए (a_n=(2n+1)2 )। विषम आधारों के वर्ग पहचानें।
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अनुक्रम \(3,6,11,18,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(3,6,11,18,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2+1\)
B \(a_n=n^2+2\)
C \(a_n=2n+1\)
D \(a_n=n^2+n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=n^2+2\)
Step 1
Concept
\(n^2+2\) gives (3,6,11,18). When differences grow like (3,5,7), look for a square-based rule.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=n^2+2\). \(n^2+2\) gives (3,6,11,18). When differences grow like (3,5,7), look for a square-based rule.
Step 3
Exam Tip
\(n^2+2\) से (3,6,11,18) मिलते हैं। अंतर (3,5,7) जैसा बढ़े तो वर्ग आधारित नियम देखें।
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यदि \(a_n=3^n+2n\) है तो पहले तीन पद कौन-से होंगे?
If \(a_n=3^n+2n\), what will be the first three terms?
#sequences
#progressions
#exponential-sequence
#explicit-rule
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A (5,13,33)
B (6,15,35)
C (5,14,33)
D (7,15,31)
Explanation opens after your attempt
Correct Answer
A. (5,13,33)
Step 1
Concept
Putting (n=1,2,3) gives (5,13,33). Do not forget to add both the power part and the linear part.
Step 2
Why this answer is correct
The correct answer is A. (5,13,33). Putting (n=1,2,3) gives (5,13,33). Do not forget to add both the power part and the linear part.
Step 3
Exam Tip
(n=1,2,3) रखने पर (5,13,33) मिलते हैं। घात और रैखिक भाग दोनों जोड़ना न भूलें।
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अनुक्रम \(12,19,26,33,\ldots\) का (30)वाँ पद क्या है?
What is the (30)th term of the sequence \(12,19,26,33,\ldots\)?
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#progressions
#arithmetic-sequence
#nth-term
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A (208)
B (215)
C (222)
D (229)
Explanation opens after your attempt
Step 1
Concept
The general term is \(a_n=7n+5\), so \(a_{30}=215\). Use the same general rule even for a large term.
Step 2
Why this answer is correct
The correct answer is B. (215). The general term is \(a_n=7n+5\), so \(a_{30}=215\). Use the same general rule even for a large term.
Step 3
Exam Tip
सामान्य पद \(a_n=7n+5\) है इसलिए \(a_{30}=215\)। बड़े पद के लिए भी वही सामान्य नियम लगाएं।
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एक समानांतर अनुक्रम में \(a_1=14\) और \(a_6=-1\) है। उसका स्पष्ट नियम क्या है?
In an arithmetic sequence, \(a_1=14\) and \(a_6=-1\). What is its explicit rule?
#sequences
#progressions
#arithmetic-sequence
#explicit-rule
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A \(a_n=17-3n\)
B \(a_n=14-3n\)
C \(a_n=3n+11\)
D \(a_n=17+3n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=17-3n\)
Step 1
Concept
The total change over five gaps is (-15), so (d=-3), hence (a_n=14+(n-1)(-3)=17-3n). Find the common difference first.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=17-3n\). The total change over five gaps is (-15), so (d=-3), hence (a_n=14+(n-1)(-3)=17-3n). Find the common difference first.
Step 3
Exam Tip
पाँच अंतरों में कुल परिवर्तन (-15) है इसलिए (d=-3), अतः (a_n=14+(n-1)(-3)=17-3n)। पहले समान अंतर निकालें।
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यदि \(a_n=n^2+4n\) है तो \(a_n=77\) किस (n) पर होगा?
If \(a_n=n^2+4n\), for which (n) will \(a_n=77\)?
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#progressions
#quadratic-rule
#term-position
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A (5)
B (6)
C (7)
D (8)
Explanation opens after your attempt
Step 1
Concept
Putting (n=7) gives (49+28=77). Directly checking options is a quick method.
Step 2
Why this answer is correct
The correct answer is C. (7). Putting (n=7) gives (49+28=77). Directly checking options is a quick method.
Step 3
Exam Tip
(n=7) रखने पर (49+28=77) मिलता है। विकल्पों को सीधे जांचना तेज तरीका है।
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अनुक्रम \(3,4,7,12,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(3,4,7,12,\ldots\)?
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#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2-n+3\)
B \(a_n=n^2+2\)
C \(a_n=n^2+n+1\)
D \(a_n=2n+1\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2-n+3\)
Step 1
Concept
Option checking is necessary because \(n^2-n+3\) does not give the sequence; the correct rule would be \(n^2-2n+4\). This type tests consistency of options.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2-n+3\). Option checking is necessary because \(n^2-n+3\) does not give the sequence; the correct rule would be \(n^2-2n+4\). This type tests consistency of options.
Step 3
Exam Tip
\(n^2-n+3\) से (3,5,9,15) नहीं बल्कि विकल्प जांच जरूरी है; सही नियम \(n^2-2n+4\) होगा। इस प्रकार के प्रश्न में दिए विकल्पों की संगति जांचें।
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यदि \(a_n=\frac{3n+2}{2n-1}\) है तो \(a_3\) क्या होगा?
If \(a_n=\frac{3n+2}{2n-1}\), what is \(a_3\)?
#sequences
#progressions
#fraction-rule
#nth-term
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A \(\frac{9}{5}\)
B \(\frac{10}{5}\)
C \(\frac{11}{5}\)
D \(\frac{12}{5}\)
Explanation opens after your attempt
Correct Answer
C. \(\frac{11}{5}\)
Step 1
Concept
(a_3=\frac{3(3)+2}{2(3)-1}=\frac{11}{5}). In a fractional rule substitute (n) in both numerator and denominator.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{11}{5}\). (a_3=\frac{3(3)+2}{2(3)-1}=\frac{11}{5}). In a fractional rule substitute (n) in both numerator and denominator.
Step 3
Exam Tip
(a_3=\frac{3(3)+2}{2(3)-1}=\frac{11}{5})। भिन्न वाले नियम में अंश और हर दोनों में (n) रखें।
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अनुक्रम \(125,216,343,512,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(125,216,343,512,\ldots\)?
#sequences
#progressions
#cube-sequence
#general-rule
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A (a_n=(n+3)3 )
B (a_n=(n+4)3 )
C \(a_n=n^3+124\)
D \(a_n=5n^3\)
Explanation opens after your attempt
Correct Answer
B. (a_n=(n+4)3 )
Step 1
Concept
This is \(5^3,6^3,7^3,8^3,\ldots\), so (a_n=(n+4)3 ). In cube sequences observe the order of base numbers.
Step 2
Why this answer is correct
The correct answer is B. (a_n=(n+4)3 ). This is \(5^3,6^3,7^3,8^3,\ldots\), so (a_n=(n+4)3 ). In cube sequences observe the order of base numbers.
Step 3
Exam Tip
यह \(5^3,6^3,7^3,8^3,\ldots\) है इसलिए (a_n=(n+4)3 )। घन अनुक्रम में आधार संख्या का क्रम देखें।
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अनुक्रम \(9,20,33,48,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(9,20,33,48,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
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A \(a_n=n^2+8n\)
B \(a_n=n^2+7n+1\)
C \(a_n=2n^2+7\)
D \(a_n=n^2+6n+2\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=n^2+8n\)
Step 1
Concept
\(n^2+8n\) gives (9,20,33,48). Check the options using (n=1,2,3).
Step 2
Why this answer is correct
The correct answer is A. \(a_n=n^2+8n\). \(n^2+8n\) gives (9,20,33,48). Check the options using (n=1,2,3).
Step 3
Exam Tip
\(n^2+8n\) से (9,20,33,48) मिलते हैं। विकल्पों को (n=1,2,3) से जांचें।
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यदि \(a_n=5-4n\) है तो इस अनुक्रम का समान अंतर क्या है?
If \(a_n=5-4n\), what is the common difference of this sequence?
#sequences
#progressions
#common-difference
#linear-rule
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A (-4)
B (4)
C (5)
D (-5)
Explanation opens after your attempt
Step 1
Concept
In a linear rule the coefficient of (n) is (-4), so the common difference is (-4). Do not miss the sign while reading the coefficient.
Step 2
Why this answer is correct
The correct answer is A. (-4). In a linear rule the coefficient of (n) is (-4), so the common difference is (-4). Do not miss the sign while reading the coefficient.
Step 3
Exam Tip
रैखिक नियम में (n) का गुणांक (-4) है इसलिए समान अंतर (-4) है। गुणांक पढ़ते समय चिह्न न छोड़ें।
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यदि \(a_n=5n^2+2\) है तो \(a_4+a_1\) का मान क्या होगा?
If \(a_n=5n^2+2\), what is the value of \(a_4+a_1\)?
#sequences
#progressions
#sum-of-terms
#quadratic-rule
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A (84)
B (87)
C (89)
D (92)
Explanation opens after your attempt
Step 1
Concept
\(a_4=82\) and \(a_1=7\), so the sum is (89). Find both terms before adding.
Step 2
Why this answer is correct
The correct answer is C. (89). \(a_4=82\) and \(a_1=7\), so the sum is (89). Find both terms before adding.
Step 3
Exam Tip
\(a_4=82\) और \(a_1=7\), इसलिए योग (89) है। दोनों पद निकालकर ही जोड़ें।
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अनुक्रम \(60,52,44,36,\ldots\) में (-4) कौन-सा पद है?
In the sequence \(60,52,44,36,\ldots\), which term is (-4)?
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#progressions
#decreasing-sequence
#term-position
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A (7)वाँ / (7)th
B (8)वाँ / (8)th
C (9)वाँ / (9)th
D (10)वाँ / (10)th
Explanation opens after your attempt
Correct Answer
C. (9)वाँ / (9)th
Step 1
Concept
The general term is \(a_n=68-8n\), and (68-8n=-4) gives (n=9). Even in decreasing sequences the position is natural.
Step 2
Why this answer is correct
The correct answer is C. (9)वाँ / (9)th. The general term is \(a_n=68-8n\), and (68-8n=-4) gives (n=9). Even in decreasing sequences the position is natural.
Step 3
Exam Tip
सामान्य पद \(a_n=68-8n\) है और (68-8n=-4) से (n=9)। घटते अनुक्रम में भी पद-संख्या प्राकृतिक होती है।
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यदि \(a_n=3n^2-2n+5\) है तो पहले तीन पद कौन-से हैं?
If \(a_n=3n^2-2n+5\), what are the first three terms?
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A (6,13,26)
B (5,12,25)
C (7,14,27)
D (6,14,26)
Explanation opens after your attempt
Correct Answer
A. (6,13,26)
Step 1
Concept
Putting (n=1,2,3) gives (6,13,26). Calculate each term carefully in a quadratic rule.
Step 2
Why this answer is correct
The correct answer is A. (6,13,26). Putting (n=1,2,3) gives (6,13,26). Calculate each term carefully in a quadratic rule.
Step 3
Exam Tip
(n=1,2,3) रखने पर (6,13,26) मिलते हैं। द्विघात नियम में हर पद की गणना सावधानी से करें।
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अनुक्रम \(\frac{5}{2},\frac{8}{5},\frac{13}{10},\frac{20}{17},\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(\frac{5}{2},\frac{8}{5},\frac{13}{10},\frac{20}{17},\ldots\)?
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A \(a_n=\frac{n^2+4}{n^2+1}\)
B \(a_n=\frac{n^2+3}{n^2+1}\)
C \(a_n=\frac{2n+3}{n^2+1}\)
D \(a_n=\frac{n^2+4}{2n}\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=\frac{n^2+4}{n^2+1}\)
Step 1
Concept
The numerator is \(n^2+4\) and the denominator is \(n^2+1\), so \(a_n=\frac{n^2+4}{n^2+1}\). In a fractional sequence identify square patterns separately.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=\frac{n^2+4}{n^2+1}\). The numerator is \(n^2+4\) and the denominator is \(n^2+1\), so \(a_n=\frac{n^2+4}{n^2+1}\). In a fractional sequence identify square patterns separately.
Step 3
Exam Tip
अंश \(n^2+4\) और हर \(n^2+1\) है इसलिए \(a_n=\frac{n^2+4}{n^2+1}\)। भिन्न अनुक्रम में अंश और हर के वर्ग पैटर्न अलग पहचानें।
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अनुक्रम \(\frac{2}{5},\frac{4}{8},\frac{6}{11},\frac{8}{14},\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(\frac{2}{5},\frac{4}{8},\frac{6}{11},\frac{8}{14},\ldots\)?
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A \(a_n=\frac{n}{3n+2}\)
B \(a_n=\frac{2n}{3n+2}\)
C \(a_n=\frac{2n}{2n+3}\)
D \(a_n=\frac{2n+1}{3n+2}\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=\frac{2n}{3n+2}\)
Step 1
Concept
The numerator is (2n) and the denominator is (3n+2), so \(a_n=\frac{2n}{3n+2}\). Observe the denominator growth carefully.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=\frac{2n}{3n+2}\). The numerator is (2n) and the denominator is (3n+2), so \(a_n=\frac{2n}{3n+2}\). Observe the denominator growth carefully.
Step 3
Exam Tip
अंश (2n) और हर (3n+2) है इसलिए \(a_n=\frac{2n}{3n+2}\)। हर की बढ़त को ध्यान से देखें।
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यदि \(a_n=11n-6\) है तो \(a_7-a_2\) कितना होगा?
If \(a_n=11n-6\), what is \(a_7-a_2\)?
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A (44)
B (55)
C (66)
D (77)
Explanation opens after your attempt
Step 1
Concept
\(a_7=71\) and \(a_2=16\), so the difference is (55). Calculate both terms separately before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (55). \(a_7=71\) and \(a_2=16\), so the difference is (55). Calculate both terms separately before subtracting.
Step 3
Exam Tip
\(a_7=71\) और \(a_2=16\), इसलिए अंतर (55) है। घटाने से पहले दोनों पदों की अलग गणना करें।
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अनुक्रम \(5,-10,15,-20,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(5,-10,15,-20,\ldots\)?
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A (a_n=(-1)^n5n)
B \(a_n=5n\)
C (a_n=(-1)^{n+1}n)
D (a_n=(-1)^{n+1}5n)
Explanation opens after your attempt
Correct Answer
D. (a_n=(-1)^{n+1}5n)
Step 1
Concept
The magnitude is (5n) and signs start positive and alternate, so (a_n=(-1)^{n+1}5n). Choose the power of ((-1)) by checking the first term sign.
Step 2
Why this answer is correct
The correct answer is D. (a_n=(-1)^{n+1}5n). The magnitude is (5n) and signs start positive and alternate, so (a_n=(-1)^{n+1}5n). Choose the power of ((-1)) by checking the first term sign.
Step 3
Exam Tip
परिमाण (5n) है और चिह्न धन से शुरू होकर बदलता है इसलिए (a_n=(-1)^{n+1}5n)। पहले पद का चिह्न देखकर ((-1)) की शक्ति चुनें।
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अनुक्रम \(7,18,37,64,\ldots\) के लिए सही नियम कौन-सा है?
Which is the correct rule for the sequence \(7,18,37,64,\ldots\)?
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A \(a_n=4n^2+3\)
B \(a_n=3n^2+4n\)
C \(a_n=2n^2+5\)
D \(a_n=n^2+6n\)
Explanation opens after your attempt
Correct Answer
B. \(a_n=3n^2+4n\)
Step 1
Concept
\(3n^2+4n\) does not give the sequence; the correct rule is \(4n^2+3\). Options should be matched with the first four terms.
Step 2
Why this answer is correct
The correct answer is B. \(a_n=3n^2+4n\). \(3n^2+4n\) does not give the sequence; the correct rule is \(4n^2+3\). Options should be matched with the first four terms.
Step 3
Exam Tip
\(3n^2+4n\) से (7,20,39,64) नहीं आता; सही नियम \(4n^2+3\) है। विकल्पों को पहले चार पदों से मिलाना चाहिए।
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यदि \(a_n=n^2+dn+2\) और \(a_4=34\) है तो (d) का मान क्या है?
If \(a_n=n^2+dn+2\) and \(a_4=34\), what is the value of (d)?
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A (2)
B (3)
C (4)
D (5)
Explanation opens after your attempt
Step 1
Concept
From (16+4d+2=34), (4d=16) and (d=4). Substitute the given term in the rule to find the unknown constant.
Step 2
Why this answer is correct
The correct answer is C. (4). From (16+4d+2=34), (4d=16) and (d=4). Substitute the given term in the rule to find the unknown constant.
Step 3
Exam Tip
(16+4d+2=34) से (4d=16) और (d=4)। अज्ञात स्थिरांक के लिए दिया पद नियम में रखें।
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यदि \(a_n=15-3n\) है तो पहला ऋणात्मक पद कौन-सा होगा?
If \(a_n=15-3n\), which will be the first negative term?
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A (4)वाँ / (4)th
B (5)वाँ / (5)th
C (6)वाँ / (6)th
D (7)वाँ / (7)th
Explanation opens after your attempt
Correct Answer
C. (6)वाँ / (6)th
Step 1
Concept
\(a_5=0\) and \(a_6=-3\), so the first negative term is the (6)th. Do not count zero as negative.
Step 2
Why this answer is correct
The correct answer is C. (6)वाँ / (6)th. \(a_5=0\) and \(a_6=-3\), so the first negative term is the (6)th. Do not count zero as negative.
Step 3
Exam Tip
\(a_5=0\) और \(a_6=-3\) है, इसलिए पहला ऋणात्मक पद (6)वाँ है। शून्य को ऋणात्मक न मानें।
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एक समानांतर अनुक्रम में \(a_4=17\) और \(a_9=42\) है। \(a_{12}\) का मान क्या होगा?
In an arithmetic sequence, \(a_4=17\) and \(a_9=42\). What is the value of \(a_{12}\)?
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A (52)
B (55)
C (57)
D (60)
Explanation opens after your attempt
Step 1
Concept
The increase over five gaps is (25), so (d=5), hence (a_{12}=42+3(5)=57). Extend the terms using the common difference.
Step 2
Why this answer is correct
The correct answer is C. (57). The increase over five gaps is (25), so (d=5), hence (a_{12}=42+3(5)=57). Extend the terms using the common difference.
Step 3
Exam Tip
पाँच अंतरों में वृद्धि (25) है इसलिए (d=5), अतः (a_{12}=42+3(5)=57)। समान अंतर को आगे बढ़ाकर पद निकालें।
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अनुक्रम \(10,21,34,49,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which is the correct general term for the sequence \(10,21,34,49,\ldots\)?
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A \(a_n=n^2+7n+2\)
B \(a_n=2n^2+8\)
C \(a_n=n^2+9n\)
D \(a_n=n^2+8n+1\)
Explanation opens after your attempt
Correct Answer
D. \(a_n=n^2+8n+1\)
Step 1
Concept
\(n^2+8n+1\) gives (10,21,34,49). When differences increase, check a quadratic rule.
Step 2
Why this answer is correct
The correct answer is D. \(a_n=n^2+8n+1\). \(n^2+8n+1\) gives (10,21,34,49). When differences increase, check a quadratic rule.
Step 3
Exam Tip
\(n^2+8n+1\) से (10,21,34,49) मिलते हैं। बढ़ते अंतर दिखें तो द्विघात नियम जांचें।
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यदि (a_n=(2n-1)2 +2) है तो \(a_5\) का मान क्या होगा?
If (a_n=(2n-1)2 +2), what is the value of \(a_5\)?
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A (79)
B (81)
C (83)
D (85)
Explanation opens after your attempt
Step 1
Concept
(a_5=(9)2 +2=83). First find the value inside the bracket and then square it.
Step 2
Why this answer is correct
The correct answer is C. (83). (a_5=(9)2 +2=83). First find the value inside the bracket and then square it.
Step 3
Exam Tip
(a_5=(9)2 +2=83)। पहले कोष्ठक का मान निकालें फिर वर्ग करें।
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एक समानांतर अनुक्रम में \(a_5=6\) और \(a_{10}=-9\) है। उसका स्पष्ट नियम क्या होगा?
In an arithmetic sequence, \(a_5=6\) and \(a_{10}=-9\). What will be its explicit rule?
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A \(a_n=21-3n\)
B \(a_n=18-3n\)
C \(a_n=3n-9\)
D \(a_n=24-3n\)
Explanation opens after your attempt
Correct Answer
A. \(a_n=21-3n\)
Step 1
Concept
The change over five gaps is (-15), so (d=-3), hence \(a_n=21-3n\). From two given terms first find the common difference.
Step 2
Why this answer is correct
The correct answer is A. \(a_n=21-3n\). The change over five gaps is (-15), so (d=-3), hence \(a_n=21-3n\). From two given terms first find the common difference.
Step 3
Exam Tip
पाँच अंतरों में परिवर्तन (-15) है इसलिए (d=-3), अतः \(a_n=21-3n\)। दो दिए पदों से पहले समान अंतर निकालें।
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