अनुक्रम \(2,9,16,23,\ldots\) का सामान्य पद कौन-सा है?
What is the general term of the sequence \(2,9,16,23,\ldots\)?
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#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 \(31,26,21,16,\ldots\)?
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#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
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#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 \(a_n=77\)?
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#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?
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#sequence-from-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))?
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#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?
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#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 \(16,25,36,49,\ldots\)?
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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 \(27,64,125,216,\ldots\)?
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#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 \(8,17,30,47,\ldots\)?
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#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
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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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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 \(4,36,100,196,\ldots\)?
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#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 \(\frac{4}{5},\frac{7}{7},\frac{10}{9},\frac{13}{11},\ldots\)?
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#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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#arithmetic-sequence
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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 \(a_n=2n^2-n+4\)?
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#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 \(6,13,22,33,\ldots\)?
#sequences
#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 \(12,19,26,33,\ldots\)?
#sequences
#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 \(a_n=77\)?
#sequences
#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 \(3,4,7,12,\ldots\)?
#sequences
#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)?
#sequences
#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?
#sequences
#progressions
#sequence-from-rule
#quadratic-rule
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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 \(\frac{5}{2},\frac{8}{5},\frac{13}{10},\frac{20}{17},\ldots\)?
#sequences
#progressions
#fraction-sequence
#general-rule
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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 \(\frac{2}{5},\frac{4}{8},\frac{6}{11},\frac{8}{14},\ldots\)?
#sequences
#progressions
#fraction-sequence
#general-rule
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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 \(a_7-a_2\)?
#sequences
#progressions
#difference-of-terms
#linear-rule
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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 \(5,-10,15,-20,\ldots\)?
#sequences
#progressions
#alternating-sequence
#general-rule
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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 \(7,18,37,64,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
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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)?
#sequences
#progressions
#unknown-coefficient
#quadratic-rule
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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?
#sequences
#progressions
#decreasing-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
\(a_5=0\) 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 \(a_{12}\)?
#sequences
#progressions
#arithmetic-sequence
#nth-term
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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 \(10,21,34,49,\ldots\)?
#sequences
#progressions
#quadratic-sequence
#general-rule
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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 \(a_5\)?
#sequences
#progressions
#odd-squares
#nth-term
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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?
#sequences
#progressions
#arithmetic-sequence
#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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