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 \(2,14,51,140,\ldots\)?
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#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
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#explicit-rule
#class-9
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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 \(82,74,66,58,\ldots\)?
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#explicit-rule
#class-9
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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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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
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#explicit-rule
#class-9
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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
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#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
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#explicit-rule
#class-9
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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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