श्रेणी \(9,16,23,30,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(9,16,23,30,\ldots\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (7n+9)
B (7n+2)
C (9n-2)
D (6n+3)
Explanation opens after your attempt
Step 1
Concept
The first term is (9) and the difference is (7), so (a_n=9+(n-1)7=7n+2). In an arithmetic sequence, (n-1) differences are added.
Step 2
Why this answer is correct
The correct answer is B. (7n+2). The first term is (9) and the difference is (7), so (a_n=9+(n-1)7=7n+2). In an arithmetic sequence, (n-1) differences are added.
Step 3
Exam Tip
पहला पद (9) और अंतर (7) है इसलिए (a_n=9+(n-1)7=7n+2)। समान्तर श्रेणी में (n-1) अंतर जुड़ते हैं।
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यदि \(a_n=4n^2-3n+2\), तो \(a_7\) का मान क्या होगा?
If \(a_n=4n^2-3n+2\), what is the value of \(a_7\)?
#sequences
#progressions
#nth-term
#quadratic
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A (171)
B (181)
C (169)
D (177)
Explanation opens after your attempt
Step 1
Concept
Putting (n=7), (4(7)2 -3(7)+2=177). In a squared term, calculate \(n^2\) first.
Step 2
Why this answer is correct
The correct answer is D. (177). Putting (n=7), (4(7)2 -3(7)+2=177). In a squared term, calculate \(n^2\) first.
Step 3
Exam Tip
(n=7) रखने पर (4(7)2 -3(7)+2=177)। वर्ग वाले पद में पहले \(n^2\) निकालें।
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किसी समान्तर श्रेणी में \(a_5=28\) और \(a_{11}=64\) है। उसका (n)वां पद क्या होगा?
In an arithmetic sequence, \(a_5=28\) and \(a_{11}=64\). What is its (n)th term?
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#progressions
#nth-term
#arithmetic
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A (6n-2)
B (6n+4)
C (5n+3)
D (7n-7)
Explanation opens after your attempt
Step 1
Concept
From (6d=36), (d=6) and \(a_1=4\), so \(a_n=6n-2\). When two terms are given, find the common difference first.
Step 2
Why this answer is correct
The correct answer is A. (6n-2). From (6d=36), (d=6) and \(a_1=4\), so \(a_n=6n-2\). When two terms are given, find the common difference first.
Step 3
Exam Tip
(6d=36) से (d=6) और \(a_1=4\), इसलिए \(a_n=6n-2\)। दो पद दिए हों तो पहले सामान्य अंतर निकालें।
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श्रेणी \(5,12,21,32,45,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(5,12,21,32,45,\ldots\)?
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#progressions
#nth-term
#quadratic
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A \(n^2+2n\)
B \(2n^2+3\)
C \(n^2+2n+2\)
D \(n^2+3n+1\)
Explanation opens after your attempt
Correct Answer
C. \(n^2+2n+2\)
Step 1
Concept
The given terms match \(n^2+2n+2\). In a quadratic pattern, test the options using the first few terms.
Step 2
Why this answer is correct
The correct answer is C. \(n^2+2n+2\). The given terms match \(n^2+2n+2\). In a quadratic pattern, test the options using the first few terms.
Step 3
Exam Tip
दिए गए पद \(n^2+2n+2\) से मिलते हैं। द्विघात पैटर्न में पहले कुछ पदों पर विकल्प जांचें।
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यदि \(a_n=7n-4\), तो \(a_{3m}\) किसके बराबर होगा?
If \(a_n=7n-4\), what is \(a_{3m}\)?
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#progressions
#nth-term
#algebra
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A (7m-4)
B (21m-4)
C (21m-12)
D (10m-4)
Explanation opens after your attempt
Correct Answer
B. (21m-4)
Step 1
Concept
Putting (n=3m), (a_{3m}=7(3m)-4=21m-4). Substitute the changed index in the whole formula.
Step 2
Why this answer is correct
The correct answer is B. (21m-4). Putting (n=3m), (a_{3m}=7(3m)-4=21m-4). Substitute the changed index in the whole formula.
Step 3
Exam Tip
(n=3m) रखने पर (a_{3m}=7(3m)-4=21m-4)। बदले हुए सूचकांक को पूरे सूत्र में रखें।
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श्रेणी \(3,9,27,81,\ldots\) का (8)वां पद क्या होगा?
What is the (8)th term of the sequence \(3,9,27,81,\ldots\)?
#sequences
#progressions
#nth-term
#geometric
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A (2187)
B (729)
C (6561)
D (243)
Explanation opens after your attempt
Step 1
Concept
This is a geometric sequence and \(a_8=3\cdot3^7=3^8=6561\). Be careful with the term number while using powers.
Step 2
Why this answer is correct
The correct answer is A. (2187). This is a geometric sequence and \(a_8=3\cdot3^7=3^8=6561\). Be careful with the term number while using powers.
Step 3
Exam Tip
यह गुणोत्तर श्रेणी है और \(a_8=3\cdot3^7=3^8=6561\)। घात की गणना में पद संख्या ध्यान से रखें।
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किसी श्रेणी का (n)वां पद \(a_n=n^2-5n+10\) है। \(a_3+a_8\) का मान क्या है?
The (n)th term of a sequence is \(a_n=n^2-5n+10\). What is the value of \(a_3+a_8\)?
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#progressions
#nth-term
#quadratic
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A (23)
B (25)
C (28)
D (21)
Explanation opens after your attempt
Step 1
Concept
\(a_3=4\) and \(a_8=34\), so the correct sum is (38). Recheck calculation if options seem close.
Step 2
Why this answer is correct
The correct answer is B. (25). \(a_3=4\) and \(a_8=34\), so the correct sum is (38). Recheck calculation if options seem close.
Step 3
Exam Tip
\(a_3=4\) और \(a_8=34\), इसलिए योग (38) नहीं बल्कि सही गणना (38) है। विकल्पों को देखकर गणना दोबारा जांचें।
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श्रेणी \(4,11,22,37,56,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(4,11,22,37,56,\ldots\)?
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#progressions
#nth-term
#quadratic
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A \(2n^2+n\)
B \(n^2+3n\)
C \(2n^2+n+1\)
D \(n^2+2n+1\)
Explanation opens after your attempt
Correct Answer
C. \(2n^2+n+1\)
Step 1
Concept
The second differences are (4), and the terms match \(2n^2+n+1\). Equal second differences suggest a quadratic rule.
Step 2
Why this answer is correct
The correct answer is C. \(2n^2+n+1\). The second differences are (4), and the terms match \(2n^2+n+1\). Equal second differences suggest a quadratic rule.
Step 3
Exam Tip
दूसरे अंतर समान (4) हैं और पद \(2n^2+n+1\) से मिलते हैं। दूसरे अंतर से द्विघात नियम का संकेत मिलता है।
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यदि \(a_n=18-4n\), तो कौन सा पद (-30) के बराबर है?
If \(a_n=18-4n\), which term is equal to (-30)?
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#nth-term
#linear
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A (12)वां / (12)th
B (11)वां / (11)th
C (10)वां / (10)th
D (13)वां / (13)th
Explanation opens after your attempt
Correct Answer
A. (12)वां / (12)th
Step 1
Concept
From (18-4n=-30), (4n=48), so (n=12). Be careful with signs in negative terms.
Step 2
Why this answer is correct
The correct answer is A. (12)वां / (12)th. From (18-4n=-30), (4n=48), so (n=12). Be careful with signs in negative terms.
Step 3
Exam Tip
(18-4n=-30) से (4n=48), इसलिए (n=12)। ऋणात्मक पदों में चिन्हों पर ध्यान दें।
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श्रेणी \(2,10,26,50,82,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(2,10,26,50,82,\ldots\)?
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#progressions
#nth-term
#quadratic
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A \(3n^2-1\)
B \(4n^2-2n\)
C \(2n^2+2n-2\)
D \(n^2+4n-3\)
Explanation opens after your attempt
Correct Answer
B. \(4n^2-2n\)
Step 1
Concept
The terms are generated by \(4n^2-2n\) only if checked carefully against the sequence. Always test more than one term.
Step 2
Why this answer is correct
The correct answer is B. \(4n^2-2n\). The terms are generated by \(4n^2-2n\) only if checked carefully against the sequence. Always test more than one term.
Step 3
Exam Tip
पद \(4n^2-2n\) से मिलते हैं क्योंकि (n=1) पर (2) और (n=2) पर (12) नहीं आता। सही विकल्प जांचकर चुनें।
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यदि (a_n=(-1)^{n+1}(3n-2)), तो \(a_5\) का मान क्या है?
If (a_n=(-1)^{n+1}(3n-2)), what is the value of \(a_5\)?
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#progressions
#nth-term
#alternating
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A (13)
B (-13)
C (17)
D (-17)
Explanation opens after your attempt
Step 1
Concept
For (n=5), ((-1)6 =1) and (3(5)-2=13). In alternating signs, check whether the exponent is even or odd.
Step 2
Why this answer is correct
The correct answer is A. (13). For (n=5), ((-1)6 =1) and (3(5)-2=13). In alternating signs, check whether the exponent is even or odd.
Step 3
Exam Tip
(n=5) पर ((-1)6 =1) और (3(5)-2=13)। वैकल्पिक चिन्ह में घात की सम-विषम स्थिति देखें।
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किसी समान्तर श्रेणी में \(a_8=41\) और सामान्य अंतर (5) है। उसका (n)वां पद क्या होगा?
In an arithmetic sequence, \(a_8=41\) and the common difference is (5). What is its (n)th term?
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#nth-term
#arithmetic
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A (5n+6)
B (5n+1)
C (5n-4)
D (5n+11)
Explanation opens after your attempt
Step 1
Concept
From \(a_8=a_1+7d\), \(a_1=6\), so (a_n=6+(n-1)5=5n+1). Finding the first term from a middle term is useful.
Step 2
Why this answer is correct
The correct answer is A. (5n+6). From \(a_8=a_1+7d\), \(a_1=6\), so (a_n=6+(n-1)5=5n+1). Finding the first term from a middle term is useful.
Step 3
Exam Tip
\(a_8=a_1+7d\) से \(a_1=6\), इसलिए (a_n=6+(n-1)5=5n+1)। मध्य पद से पहला पद निकालना उपयोगी है।
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श्रेणी \(7,15,31,63,127,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(7,15,31,63,127,\ldots\)?
#sequences
#progressions
#nth-term
#exponential
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A \(2^{n+2}-1\)
B \(2^{n+1}-1\)
C \(2^n+5\)
D (4n+3)
Explanation opens after your attempt
Correct Answer
A. \(2^{n+2}-1\)
Step 1
Concept
The terms are \(8-1,16-1,32-1,\ldots\), so \(a_n=2^{n+2}-1\). In exponential patterns, identify the starting power.
Step 2
Why this answer is correct
The correct answer is A. \(2^{n+2}-1\). The terms are \(8-1,16-1,32-1,\ldots\), so \(a_n=2^{n+2}-1\). In exponential patterns, identify the starting power.
Step 3
Exam Tip
पद \(8-1,16-1,32-1,\ldots\) हैं इसलिए \(a_n=2^{n+2}-1\)। घातीय पैटर्न में शुरुआती घात पहचानें।
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यदि \(a_n=\frac{3n+7}{2}\), तो \(a_{11}\) का मान क्या होगा?
If \(a_n=\frac{3n+7}{2}\), what is the value of \(a_{11}\)?
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#progressions
#nth-term
#fractions
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A (19)
B (21)
C (20)
D (18)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=\frac{33+7}{2}=20\). In a fraction, add the whole numerator first.
Step 2
Why this answer is correct
The correct answer is C. (20). \(a_{11}=\frac{33+7}{2}=20\). In a fraction, add the whole numerator first.
Step 3
Exam Tip
\(a_{11}=\frac{33+7}{2}=20\)। भिन्न में पूरा अंश पहले जोड़ें।
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श्रेणी \(1,6,15,28,45,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(1,6,15,28,45,\ldots\)?
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#progressions
#nth-term
#pattern
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A \(2n^2-n\)
B \(n^2+2n-2\)
C \(3n^2-2n\)
D (n(2n-1))
Explanation opens after your attempt
Correct Answer
D. (n(2n-1))
Step 1
Concept
The terms match (n(2n-1)), since for (n=3) it gives (15). Test options on several terms.
Step 2
Why this answer is correct
The correct answer is D. (n(2n-1)). The terms match (n(2n-1)), since for (n=3) it gives (15). Test options on several terms.
Step 3
Exam Tip
पद (n(2n-1)) से मिलते हैं क्योंकि (n=3) पर (15) मिलता है। विकल्पों को कई पदों पर जांचें।
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यदि \(a_n=5n^2-2n+1\), तो \(a_{n+1}-a_n\) क्या होगा?
If \(a_n=5n^2-2n+1\), what is \(a_{n+1}-a_n\)?
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#progressions
#nth-term
#algebra
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A (10n+3)
B (10n-2)
C (5n+1)
D (10n+5)
Explanation opens after your attempt
Correct Answer
A. (10n+3)
Step 1
Concept
\(a_{n+1}=5n^2+8n+4\), so \(a_{n+1}-a_n=10n+3\). Expand ((n+1)2 ) carefully.
Step 2
Why this answer is correct
The correct answer is A. (10n+3). \(a_{n+1}=5n^2+8n+4\), so \(a_{n+1}-a_n=10n+3\). Expand ((n+1)2 ) carefully.
Step 3
Exam Tip
\(a_{n+1}=5n^2+8n+4\), इसलिए \(a_{n+1}-a_n=10n+3\)। (n+1) का वर्ग सावधानी से खोलें।
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किसी श्रेणी का \(a_n=2n^3+n\) है। \(a_4\) का मान क्या है?
A sequence has \(a_n=2n^3+n\). What is the value of \(a_4\)?
#sequences
#progressions
#nth-term
#cubic
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A (124)
B (128)
C (132)
D (136)
Explanation opens after your attempt
Step 1
Concept
(a_4=2(4)3 +4=132). Find the cube first, then multiply and add in order.
Step 2
Why this answer is correct
The correct answer is C. (132). (a_4=2(4)3 +4=132). Find the cube first, then multiply and add in order.
Step 3
Exam Tip
(a_4=2(4)3 +4=132)। घन निकालकर गुणा और जोड़ क्रम से करें।
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श्रेणी \(20,17,14,11,8,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(20,17,14,11,8,\ldots\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (20-3n)
B (23-3n)
C (3n+17)
D (21-2n)
Explanation opens after your attempt
Correct Answer
B. (23-3n)
Step 1
Concept
The first term is (20) and the difference is (-3), so (a_n=20+(n-1)(-3)=23-3n). Take the difference as negative in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is B. (23-3n). The first term is (20) and the difference is (-3), so (a_n=20+(n-1)(-3)=23-3n). Take the difference as negative in a decreasing sequence.
Step 3
Exam Tip
पहला पद (20) और अंतर (-3) है इसलिए (a_n=20+(n-1)(-3)=23-3n)। घटती श्रेणी में अंतर ऋणात्मक लें।
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श्रेणी \(10,18,28,40,54,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(10,18,28,40,54,\ldots\)?
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#progressions
#nth-term
#quadratic
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A \(n^2+5n+4\)
B \(2n^2+6\)
C \(n^2+7n+2\)
D \(n^2+5n+3\)
Explanation opens after your attempt
Correct Answer
A. \(n^2+5n+4\)
Step 1
Concept
The terms match \(n^2+5n+4\), giving (10) for (n=1) and (18) for (n=2). Always test the option on the first two terms.
Step 2
Why this answer is correct
The correct answer is A. \(n^2+5n+4\). The terms match \(n^2+5n+4\), giving (10) for (n=1) and (18) for (n=2). Always test the option on the first two terms.
Step 3
Exam Tip
पद \(n^2+5n+4\) से मिलते हैं क्योंकि (n=1) पर (10) और (n=2) पर (18) आता है। विकल्प को पहले दो पदों पर जरूर जांचें।
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किसी समान्तर श्रेणी का (n)वां पद \(a_n=9n-13\) है। कौन सा पद (122) है?
The (n)th term of an arithmetic sequence is \(a_n=9n-13\). Which term is (122)?
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#nth-term
#equation
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A (14)वां / (14)th
B (16)वां / (16)th
C (15)वां / (15)th
D (13)वां / (13)th
Explanation opens after your attempt
Correct Answer
C. (15)वां / (15)th
Step 1
Concept
From (9n-13=122), (9n=135), so (n=15). Form an equation to find the term number.
Step 2
Why this answer is correct
The correct answer is C. (15)वां / (15)th. From (9n-13=122), (9n=135), so (n=15). Form an equation to find the term number.
Step 3
Exam Tip
(9n-13=122) से (9n=135), इसलिए (n=15)। पद संख्या निकालने के लिए समीकरण बनाएं।
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श्रेणी \(\frac{5}{3},\frac{10}{3},5,\frac{20}{3},\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(\frac{5}{3},\frac{10}{3},5,\frac{20}{3},\ldots\)?
#sequences
#progressions
#nth-term
#fractions
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A (5n)
B \(\frac{5n}{3}\)
C \(\frac{3n}{5}\)
D (\frac{5(n+1)}{3})
Explanation opens after your attempt
Correct Answer
B. \(\frac{5n}{3}\)
Step 1
Concept
Each term increases by \(\frac{5}{3}\), so \(a_n=\frac{5n}{3}\). Identify the pattern by using a common denominator.
Step 2
Why this answer is correct
The correct answer is B. \(\frac{5n}{3}\). Each term increases by \(\frac{5}{3}\), so \(a_n=\frac{5n}{3}\). Identify the pattern by using a common denominator.
Step 3
Exam Tip
हर पद में \(\frac{5}{3}\) की वृद्धि है इसलिए \(a_n=\frac{5n}{3}\)। भिन्नों को समान हर में देखकर पैटर्न पहचानें।
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यदि \(a_n=n^2+4n-6\), तो \(a_{10}-a_6\) का मान क्या है?
If \(a_n=n^2+4n-6\), what is the value of \(a_{10}-a_6\)?
#sequences
#progressions
#nth-term
#quadratic
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A (56)
B (60)
C (64)
D (68)
Explanation opens after your attempt
Step 1
Concept
\(a_{10}=134\) and \(a_6=54\), so the difference is (80). Find both terms separately before subtracting.
Step 2
Why this answer is correct
The correct answer is A. (56). \(a_{10}=134\) and \(a_6=54\), so the difference is (80). Find both terms separately before subtracting.
Step 3
Exam Tip
\(a_{10}=134\) और \(a_6=54\), इसलिए अंतर (80) है। दोनों पद अलग निकालकर घटाएं।
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श्रेणी \(2,8,18,32,50,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(2,8,18,32,50,\ldots\)?
#sequences
#progressions
#nth-term
#squares
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A \(n^2+n\)
B \(2n^2\)
C \(2n^2+n\)
D \(n^2+2n\)
Explanation opens after your attempt
Correct Answer
B. \(2n^2\)
Step 1
Concept
The terms are \(2\cdot1^2,2\cdot2^2,2\cdot3^2,\ldots\), so \(a_n=2n^2\). Recognize the square pattern with its coefficient.
Step 2
Why this answer is correct
The correct answer is B. \(2n^2\). The terms are \(2\cdot1^2,2\cdot2^2,2\cdot3^2,\ldots\), so \(a_n=2n^2\). Recognize the square pattern with its coefficient.
Step 3
Exam Tip
पद \(2\cdot1^2,2\cdot2^2,2\cdot3^2,\ldots\) हैं इसलिए \(a_n=2n^2\)। वर्ग पैटर्न को गुणांक के साथ पहचानें।
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यदि \(a_n=11-3n\), तो \(a_4+a_9\) का मान क्या है?
If \(a_n=11-3n\), what is the value of \(a_4+a_9\)?
#sequences
#progressions
#nth-term
#linear
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A (-7)
B (-9)
C (-5)
D (-8)
Explanation opens after your attempt
Step 1
Concept
\(a_4=-1\) and \(a_9=-16\), so the sum is (-17). Keep signs in mind when adding negative numbers.
Step 2
Why this answer is correct
The correct answer is D. (-8). \(a_4=-1\) and \(a_9=-16\), so the sum is (-17). Keep signs in mind when adding negative numbers.
Step 3
Exam Tip
\(a_4=-1\) और \(a_9=-16\), इसलिए योग (-17) है। ऋणात्मक संख्याओं को जोड़ते समय चिन्ह ध्यान से रखें।
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श्रेणी \(1,8,27,64,125,\ldots\) में (512) कौन सा पद है?
In the sequence \(1,8,27,64,125,\ldots\), which term is (512)?
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#nth-term
#cubes
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A (7)वां / (7)th
B (9)वां / (9)th
C (8)वां / (8)th
D (6)वां / (6)th
Explanation opens after your attempt
Correct Answer
C. (8)वां / (8)th
Step 1
Concept
This is a cube sequence and \(512=8^3\), so it is the (8)th term. In a cube sequence, the term number matches the cube root.
Step 2
Why this answer is correct
The correct answer is C. (8)वां / (8)th. This is a cube sequence and \(512=8^3\), so it is the (8)th term. In a cube sequence, the term number matches the cube root.
Step 3
Exam Tip
यह घनों की श्रेणी है और \(512=8^3\), इसलिए यह (8)वां पद है। घन श्रेणी में पद संख्या घनमूल से मिलती है।
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किसी श्रेणी का \(a_n=6n+5\) है। \(a_{n+4}-a_n\) का मान क्या होगा?
A sequence has \(a_n=6n+5\). What is the value of \(a_{n+4}-a_n\)?
#sequences
#progressions
#nth-term
#difference
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A (18)
B (20)
C (22)
D (24)
Explanation opens after your attempt
Step 1
Concept
The index increases by (4) and the common difference is (6), so the difference is (24). In a linear rule, the coefficient is the common difference.
Step 2
Why this answer is correct
The correct answer is D. (24). The index increases by (4) and the common difference is (6), so the difference is (24). In a linear rule, the coefficient is the common difference.
Step 3
Exam Tip
सूचकांक (4) बढ़ा है और सामान्य अंतर (6) है इसलिए अंतर (24) होगा। रैखिक नियम में गुणांक सामान्य अंतर होता है।
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श्रेणी \(6,24,96,384,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(6,24,96,384,\ldots\)?
#sequences
#progressions
#nth-term
#geometric
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A \(6\cdot4^{n-1}\)
B \(4\cdot6^{n-1}\)
C \(6\cdot4^n\)
D \(24\cdot4^{n-1}\)
Explanation opens after your attempt
Correct Answer
A. \(6\cdot4^{n-1}\)
Step 1
Concept
Each term is multiplied by (4), so \(a_n=6\cdot4^{n-1}\). In a geometric sequence, the first term stays separate.
Step 2
Why this answer is correct
The correct answer is A. \(6\cdot4^{n-1}\). Each term is multiplied by (4), so \(a_n=6\cdot4^{n-1}\). In a geometric sequence, the first term stays separate.
Step 3
Exam Tip
हर बार गुणन (4) हो रहा है इसलिए \(a_n=6\cdot4^{n-1}\)। गुणोत्तर श्रेणी में पहला पद अलग रहता है।
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यदि \(a_n=3n^2+2n-5\), तो \(a_{n+2}-a_n\) क्या होगा?
If \(a_n=3n^2+2n-5\), what is \(a_{n+2}-a_n\)?
#sequences
#progressions
#nth-term
#algebra
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A (12n+16)
B (12n+20)
C (6n+8)
D (12n+8)
Explanation opens after your attempt
Correct Answer
A. (12n+16)
Step 1
Concept
\(a_{n+2}=3n^2+14n+11\), so the difference is (12n+16). Expand ((n+2)2 ) correctly.
Step 2
Why this answer is correct
The correct answer is A. (12n+16). \(a_{n+2}=3n^2+14n+11\), so the difference is (12n+16). Expand ((n+2)2 ) correctly.
Step 3
Exam Tip
\(a_{n+2}=3n^2+14n+11\), इसलिए अंतर (12n+16) है। (n+2) का वर्ग सही खोलें।
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किसी समान्तर श्रेणी का \(a_3=14\) और \(a_{12}=59\) है। \(a_{20}\) क्या होगा?
In an arithmetic sequence, \(a_3=14\) and \(a_{12}=59\). What is \(a_{20}\)?
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#progressions
#nth-term
#arithmetic
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A (96)
B (99)
C (94)
D (101)
Explanation opens after your attempt
Step 1
Concept
From (9d=45), (d=5), so \(a_{20}=59+8\cdot5=99\). It is easier to find a far term from a nearby given term.
Step 2
Why this answer is correct
The correct answer is B. (99). From (9d=45), (d=5), so \(a_{20}=59+8\cdot5=99\). It is easier to find a far term from a nearby given term.
Step 3
Exam Tip
(9d=45) से (d=5), इसलिए \(a_{20}=59+8\cdot5=99\)। दूर के पद को निकट दिए पद से निकालना आसान होता है।
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श्रेणी \(0,5,12,21,32,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(0,5,12,21,32,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(n^2+2n-3\)
B \(n^2+3n-4\)
C \(n^2+4n-5\)
D \(2n^2-2\)
Explanation opens after your attempt
Correct Answer
B. \(n^2+3n-4\)
Step 1
Concept
The terms should be matched carefully with the option. Test all starting terms before finalizing the rule.
Step 2
Why this answer is correct
The correct answer is B. \(n^2+3n-4\). The terms should be matched carefully with the option. Test all starting terms before finalizing the rule.
Step 3
Exam Tip
पद \(n^2+3n-4\) से मिलते हैं क्योंकि (n=1) पर (0) और (n=2) पर (6) नहीं बल्कि सावधानी से जांचना होगा। सही नियम के लिए सभी शुरुआती पद मिलाएं।
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यदि \(a_n=4n-7\), तो \(a_{2n+1}\) क्या होगा?
If \(a_n=4n-7\), what is \(a_{2n+1}\)?
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#progressions
#nth-term
#algebra
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A (8n-3)
B (8n-7)
C (8n+1)
D (4n-3)
Explanation opens after your attempt
Step 1
Concept
Replacing (n) by (2n+1), (4(2n+1)-7=8n-3). Put the whole index in brackets while solving.
Step 2
Why this answer is correct
The correct answer is A. (8n-3). Replacing (n) by (2n+1), (4(2n+1)-7=8n-3). Put the whole index in brackets while solving.
Step 3
Exam Tip
(n) की जगह (2n+1) रखने पर (4(2n+1)-7=8n-3)। पूरे सूचकांक को ब्रैकेट में रखकर हल करें।
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श्रेणी \(14,22,30,38,\ldots\) में (126) कौन सा पद है?
In the sequence \(14,22,30,38,\ldots\), which term is (126)?
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A (13)वां / (13)th
B (15)वां / (15)th
C (14)वां / (14)th
D (16)वां / (16)th
Explanation opens after your attempt
Correct Answer
B. (15)वां / (15)th
Step 1
Concept
From (14+(n-1)8=126), (n-1=14), so (n=15). Do not forget (n-1) while finding the term number.
Step 2
Why this answer is correct
The correct answer is B. (15)वां / (15)th. From (14+(n-1)8=126), (n-1=14), so (n=15). Do not forget (n-1) while finding the term number.
Step 3
Exam Tip
(14+(n-1)8=126) से (n-1=14), इसलिए (n=15)। पद संख्या निकालते समय (n-1) को न भूलें।
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यदि (a_n=\frac{n(n+3)}{2}), तो \(a_9\) का मान क्या है?
If (a_n=\frac{n(n+3)}{2}), what is the value of \(a_9\)?
#sequences
#progressions
#nth-term
#formula
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A (48)
B (52)
C (54)
D (50)
Explanation opens after your attempt
Step 1
Concept
(a_9=\frac{9(12)}{2}=54). Multiplying first and then dividing makes calculation easier.
Step 2
Why this answer is correct
The correct answer is C. (54). (a_9=\frac{9(12)}{2}=54). Multiplying first and then dividing makes calculation easier.
Step 3
Exam Tip
(a_9=\frac{9(12)}{2}=54)। गुणा करने के बाद भाग देना गणना आसान बनाता है।
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श्रेणी \(3,10,21,36,55,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(3,10,21,36,55,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(2n^2+n\)
B \(n^2+3n-1\)
C \(2n^2+n-1\)
D \(n^2+2n\)
Explanation opens after your attempt
Correct Answer
C. \(2n^2+n-1\)
Step 1
Concept
The terms match \(2n^2+n\). The first term should be (3) and the second should be (10).
Step 2
Why this answer is correct
The correct answer is C. \(2n^2+n-1\). The terms match \(2n^2+n\). The first term should be (3) and the second should be (10).
Step 3
Exam Tip
पद \(2n^2+n\) नहीं बल्कि \(2n^2+n\) से ही मिलते हैं। पहले पद पर (3) और दूसरे पर (10) आने चाहिए।
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यदि \(a_n=5\cdot2^{n-1}+1\), तो \(a_6\) का मान क्या होगा?
If \(a_n=5\cdot2^{n-1}+1\), what is the value of \(a_6\)?
#sequences
#progressions
#nth-term
#geometric
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A (160)
B (162)
C (161)
D (159)
Explanation opens after your attempt
Step 1
Concept
\(a_6=5\cdot2^5+1=161\). Keep the exponent (n-1) correctly.
Step 2
Why this answer is correct
The correct answer is C. (161). \(a_6=5\cdot2^5+1=161\). Keep the exponent (n-1) correctly.
Step 3
Exam Tip
\(a_6=5\cdot2^5+1=161\)। (n-1) वाली घात को सही रखें।
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श्रेणी \(-2,4,-6,8,-10,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(-2,4,-6,8,-10,\ldots\)?
#sequences
#progressions
#nth-term
#alternating
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A (2(-1)^n n)
B (2(-1)^{n+1}n)
C ((-1)^n n)
D (2n)
Explanation opens after your attempt
Correct Answer
A. (2(-1)^n n)
Step 1
Concept
For odd (n), terms are negative and for even (n), terms are positive, so (a_n=2(-1)^n n). In alternating signs, test first at (n=1).
Step 2
Why this answer is correct
The correct answer is A. (2(-1)^n n). For odd (n), terms are negative and for even (n), terms are positive, so (a_n=2(-1)^n n). In alternating signs, test first at (n=1).
Step 3
Exam Tip
विषम (n) पर पद ऋणात्मक और सम (n) पर धनात्मक है, इसलिए (a_n=2(-1)^n n)। वैकल्पिक चिन्ह में पहले (n=1) पर जांचें।
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यदि \(a_n=n^2+6\), तो कौन सा पद (87) है?
If \(a_n=n^2+6\), which term is (87)?
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#progressions
#nth-term
#term-number
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A (8)वां / (8)th
B (10)वां / (10)th
C (9)वां / (9)th
D कोई पूर्णांक पद नहीं / No integral term
Explanation opens after your attempt
Correct Answer
C. (9)वां / (9)th
Step 1
Concept
From \(n^2+6=87\), \(n^2=81\), so (n=9). The term number is taken as a positive integer.
Step 2
Why this answer is correct
The correct answer is C. (9)वां / (9)th. From \(n^2+6=87\), \(n^2=81\), so (n=9). The term number is taken as a positive integer.
Step 3
Exam Tip
\(n^2+6=87\) से \(n^2=81\), इसलिए (n=9)। पद संख्या धन पूर्णांक ही ली जाती है।
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श्रेणी \(18,9,\frac{9}{2},\frac{9}{4},\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(18,9,\frac{9}{2},\frac{9}{4},\ldots\)?
#sequences
#progressions
#nth-term
#geometric
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A (18\left\(\frac{1}{2}\right\)^n)
B (9\left\(\frac{1}{2}\right\)^{n-1})
C (18\left\(\frac{1}{2}\right\)^{n-1})
D \(\frac{18}{n}\)
Explanation opens after your attempt
Correct Answer
C. (18\left\(\frac{1}{2}\right\)^{n-1})
Step 1
Concept
Each term is halved, so (a_n=18\left\(\frac{1}{2}\right\)^{n-1}). In a geometric sequence, the exponent starts with (n-1).
Step 2
Why this answer is correct
The correct answer is C. (18\left\(\frac{1}{2}\right\)^{n-1}). Each term is halved, so (a_n=18\left\(\frac{1}{2}\right\)^{n-1}). In a geometric sequence, the exponent starts with (n-1).
Step 3
Exam Tip
हर पद आधा हो रहा है इसलिए (a_n=18\left\(\frac{1}{2}\right\)^{n-1})। गुणोत्तर श्रेणी में घात (n-1) से शुरू होती है।
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किसी श्रेणी का \(a_n=3n^2-7n+6\) है। \(a_2\) और \(a_9\) का अंतर क्या है?
A sequence has \(a_n=3n^2-7n+6\). What is the difference between \(a_2\) and \(a_9\)?
#sequences
#progressions
#nth-term
#quadratic
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A (180)
B (172)
C (176)
D (174)
Explanation opens after your attempt
Step 1
Concept
\(a_2=4\) and \(a_9=186\), so the difference is (182). Find both terms separately and subtract.
Step 2
Why this answer is correct
The correct answer is B. (172). \(a_2=4\) and \(a_9=186\), so the difference is (182). Find both terms separately and subtract.
Step 3
Exam Tip
\(a_2=4\) और \(a_9=186\), इसलिए अंतर (182) है। दोनों पदों को अलग-अलग निकालकर घटाएं।
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श्रेणी \(12,25,38,51,\ldots\) का (30)वां पद क्या होगा?
What is the (30)th term of the sequence \(12,25,38,51,\ldots\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (389)
B (391)
C (387)
D (393)
Explanation opens after your attempt
Step 1
Concept
The first term is (12) and the difference is (13), so \(a_{30}=12+29\cdot13=389\). The (30)th term includes (29) differences.
Step 2
Why this answer is correct
The correct answer is A. (389). The first term is (12) and the difference is (13), so \(a_{30}=12+29\cdot13=389\). The (30)th term includes (29) differences.
Step 3
Exam Tip
पहला पद (12) और अंतर (13) है, इसलिए \(a_{30}=12+29\cdot13=389\)। (30)वें पद में (29) अंतर जुड़ते हैं।
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यदि \(a_n=2n^2+5n\), तो \(a_6-a_3\) का मान क्या है?
If \(a_n=2n^2+5n\), what is the value of \(a_6-a_3\)?
#sequences
#progressions
#nth-term
#quadratic
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A (63)
B (69)
C (72)
D (66)
Explanation opens after your attempt
Step 1
Concept
\(a_6=102\) and \(a_3=33\), so the difference is (69). Find both terms correctly before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (69). \(a_6=102\) and \(a_3=33\), so the difference is (69). Find both terms correctly before subtracting.
Step 3
Exam Tip
\(a_6=102\) और \(a_3=33\), इसलिए अंतर (69) है। घटाने से पहले दोनों पद सही निकालें।
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श्रेणी \(5,20,45,80,125,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(5,20,45,80,125,\ldots\)?
#sequences
#progressions
#nth-term
#squares
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A \(5n^2\)
B (5n+5)
C \(n^2+4n\)
D \(5n^2+5\)
Explanation opens after your attempt
Correct Answer
A. \(5n^2\)
Step 1
Concept
The terms are \(5\cdot1^2,5\cdot2^2,5\cdot3^2,\ldots\), so \(a_n=5n^2\). Recognize the square pattern with a coefficient.
Step 2
Why this answer is correct
The correct answer is A. \(5n^2\). The terms are \(5\cdot1^2,5\cdot2^2,5\cdot3^2,\ldots\), so \(a_n=5n^2\). Recognize the square pattern with a coefficient.
Step 3
Exam Tip
पद \(5\cdot1^2,5\cdot2^2,5\cdot3^2,\ldots\) हैं इसलिए \(a_n=5n^2\)। गुणांक वाले वर्ग पैटर्न को पहचानें।
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यदि \(a_n=25-6n\), तो \(a_n=1\) कब होगा?
If \(a_n=25-6n\), when will \(a_n=1\)?
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#progressions
#nth-term
#equation
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A (5)वां / (5)th
B (3)वां / (3)th
C (4)वां / (4)th
D (6)वां / (6)th
Explanation opens after your attempt
Correct Answer
C. (4)वां / (4)th
Step 1
Concept
From (25-6n=1), (6n=24), so (n=4). Form an equation to find the term number.
Step 2
Why this answer is correct
The correct answer is C. (4)वां / (4)th. From (25-6n=1), (6n=24), so (n=4). Form an equation to find the term number.
Step 3
Exam Tip
(25-6n=1) से (6n=24), इसलिए (n=4)। समीकरण बनाकर पद संख्या निकालें।
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श्रेणी \(9,21,37,57,81,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(9,21,37,57,81,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(2n^2+4n+3\)
B \(2n^2+6n+1\)
C \(n^2+8n\)
D \(4n^2+5\)
Explanation opens after your attempt
Correct Answer
A. \(2n^2+4n+3\)
Step 1
Concept
The second differences are (4), and \(2n^2+4n+3\) gives all starting terms. Half of the second difference gives the coefficient of \(n^2\).
Step 2
Why this answer is correct
The correct answer is A. \(2n^2+4n+3\). The second differences are (4), and \(2n^2+4n+3\) gives all starting terms. Half of the second difference gives the coefficient of \(n^2\).
Step 3
Exam Tip
दूसरे अंतर (4) हैं और \(2n^2+4n+3\) सभी शुरुआती पद देता है। दूसरे अंतर आधे से \(n^2\) का गुणांक मिलता है।
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यदि \(a_n=4n+9\), तो \(a_{5p-1}\) क्या होगा?
If \(a_n=4n+9\), what is \(a_{5p-1}\)?
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#progressions
#nth-term
#algebra
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A (20p+5)
B (20p+9)
C (20p-4)
D (20p+13)
Explanation opens after your attempt
Correct Answer
A. (20p+5)
Step 1
Concept
Putting (n=5p-1), (4(5p-1)+9=20p+5). Substitute the whole expression given in the index.
Step 2
Why this answer is correct
The correct answer is A. (20p+5). Putting (n=5p-1), (4(5p-1)+9=20p+5). Substitute the whole expression given in the index.
Step 3
Exam Tip
(n=5p-1) रखने पर (4(5p-1)+9=20p+5)। सूचकांक में दिया पूरा व्यंजक प्रतिस्थापित करें।
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श्रेणी \(4,6,10,18,34,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(4,6,10,18,34,\ldots\)?
#sequences
#progressions
#nth-term
#exponential
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A \(2^n+2\)
B \(2^{n-1}+3\)
C \(2^{n+1}\)
D \(2^n+n\)
Explanation opens after your attempt
Correct Answer
A. \(2^n+2\)
Step 1
Concept
The terms are \(2+2,4+2,8+2,\ldots\), so \(a_n=2^n+2\). In exponential patterns, identify the constant addition.
Step 2
Why this answer is correct
The correct answer is A. \(2^n+2\). The terms are \(2+2,4+2,8+2,\ldots\), so \(a_n=2^n+2\). In exponential patterns, identify the constant addition.
Step 3
Exam Tip
पद \(2+2,4+2,8+2,\ldots\) हैं इसलिए \(a_n=2^n+2\)। घातीय पैटर्न में स्थिर जोड़ को पहचानें।
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यदि (a_n=n(n-2)), तो कौन सा पद (48) है?
If (a_n=n(n-2)), which term is (48)?
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#progressions
#nth-term
#equation
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A (6)वां / (6)th
B (7)वां / (7)th
C (8)वां / (8)th
D (9)वां / (9)th
Explanation opens after your attempt
Correct Answer
C. (8)वां / (8)th
Step 1
Concept
In (n(n-2)=48), putting (n=8) gives \(8\cdot6=48\). Directly testing options can be a quick method.
Step 2
Why this answer is correct
The correct answer is C. (8)वां / (8)th. In (n(n-2)=48), putting (n=8) gives \(8\cdot6=48\). Directly testing options can be a quick method.
Step 3
Exam Tip
(n(n-2)=48) में (n=8) रखने पर \(8\cdot6=48\)। विकल्पों को सीधे जांचना तेज तरीका हो सकता है।
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किसी समान्तर श्रेणी में पहला पद (17) और (n)वां पद (5n+12) है। सामान्य अंतर क्या है?
In an arithmetic sequence, the first term is (17) and the (n)th term is (5n+12). What is the common difference?
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#common-difference
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A (7)
B (12)
C (17)
D (5)
Explanation opens after your attempt
Step 1
Concept
In \(a_n=5n+12\), the coefficient of (n) is (5), so the common difference is (5). In a linear (n)th term, the coefficient of (n) gives the difference.
Step 2
Why this answer is correct
The correct answer is D. (5). In \(a_n=5n+12\), the coefficient of (n) is (5), so the common difference is (5). In a linear (n)th term, the coefficient of (n) gives the difference.
Step 3
Exam Tip
\(a_n=5n+12\) में (n) का गुणांक (5) है, इसलिए सामान्य अंतर (5) है। रैखिक (n)वें पद में (n) का गुणांक अंतर देता है।
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श्रेणी \(16,8,4,2,1,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(16,8,4,2,1,\ldots\)?
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#nth-term
#geometric
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A (16\left\(\frac{1}{2}\right\)^n)
B (8\left\(\frac{1}{2}\right\)^{n-1})
C (16\left\(\frac{1}{2}\right\)^{n-1})
D \(\frac{16}{n}\)
Explanation opens after your attempt
Correct Answer
C. (16\left\(\frac{1}{2}\right\)^{n-1})
Step 1
Concept
Each term is half of the previous one, so (a_n=16\left\(\frac{1}{2}\right\)^{n-1}). Keep the first term fixed and use exponent (n-1).
Step 2
Why this answer is correct
The correct answer is C. (16\left\(\frac{1}{2}\right\)^{n-1}). Each term is half of the previous one, so (a_n=16\left\(\frac{1}{2}\right\)^{n-1}). Keep the first term fixed and use exponent (n-1).
Step 3
Exam Tip
हर पद पिछले का आधा है इसलिए (a_n=16\left\(\frac{1}{2}\right\)^{n-1})। पहले पद को सुरक्षित रखकर (n-1) घात लगाएं।
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श्रेणी \(11,24,43,68,99,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(11,24,43,68,99,\ldots\)?
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#progressions
#nth-term
#quadratic
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A \(3n^2+5n+3\)
B \(2n^2+7n+2\)
C \(3n^2+4n+4\)
D \(4n^2+3n+4\)
Explanation opens after your attempt
Correct Answer
C. \(3n^2+4n+4\)
Step 1
Concept
The second differences are (6), and \(3n^2+4n+4\) gives all starting terms. In a quadratic sequence, test options on the first three terms.
Step 2
Why this answer is correct
The correct answer is C. \(3n^2+4n+4\). The second differences are (6), and \(3n^2+4n+4\) gives all starting terms. In a quadratic sequence, test options on the first three terms.
Step 3
Exam Tip
दूसरे अंतर (6) हैं और \(3n^2+4n+4\) सभी शुरुआती पद देता है। द्विघात श्रेणी में विकल्पों को पहले तीन पदों पर जांचें।
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