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
#class-9
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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 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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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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अनुक्रम \(\frac{5}{2},6,\frac{21}{2},16,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(\frac{5}{2},6,\frac{21}{2},16,\ldots\)?
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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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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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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)?
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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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अनुक्रम \(3,16,41,78,\ldots\) का सामान्य पद क्या है?
What is the general term of the sequence \(3,16,41,78,\ldots\)?
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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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अनुक्रम \(7,14,27,52,\ldots\) के लिए सही सामान्य पद कौन-सा है?
Which general term is correct for the sequence \(7,14,27,52,\ldots\)?
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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)?
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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?
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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 \(2,13,24,35,\ldots\) 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?
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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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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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? Hint Small clue
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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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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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
50 50-50 2 wrong hide
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? Hint Small clue
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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