श्रेणी \(17,25,33,41,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(17,25,33,41,\ldots\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (8n+17)
B (9n+8)
C (8n+9)
D (17n-8)
Explanation opens after your attempt
Step 1
Concept
The first term is (17) and the difference is (8), so (a_n=17+(n-1)8=8n+9). In an arithmetic sequence, (n-1) differences are added.
Step 2
Why this answer is correct
The correct answer is C. (8n+9). The first term is (17) and the difference is (8), so (a_n=17+(n-1)8=8n+9). In an arithmetic sequence, (n-1) differences are added.
Step 3
Exam Tip
पहला पद (17) और अंतर (8) है, इसलिए (a_n=17+(n-1)8=8n+9)। समान्तर श्रेणी में (n-1) अंतर जुड़ते हैं।
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यदि \(a_n=7n^2-3n+5\), तो \(a_6\) का मान क्या होगा?
If \(a_n=7n^2-3n+5\), what is the value of \(a_6\)?
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#progressions
#nth-term
#quadratic
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A (239)
B (245)
C (252)
D (248)
Explanation opens after your attempt
Step 1
Concept
(a_6=7(6)2 -3(6)+5=239). In a squared term, calculate \(n^2\) first.
Step 2
Why this answer is correct
The correct answer is A. (239). (a_6=7(6)2 -3(6)+5=239). In a squared term, calculate \(n^2\) first.
Step 3
Exam Tip
(a_6=7(6)2 -3(6)+5=239)। वर्ग वाले पद में पहले \(n^2\) निकालें।
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किसी समान्तर श्रेणी में \(a_6=47\) और \(a_{13}=110\) है। उसका (n)वां पद क्या होगा?
In an arithmetic sequence, \(a_6=47\) and \(a_{13}=110\). What is its (n)th term?
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#progressions
#nth-term
#arithmetic
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A (9n+2)
B (9n-7)
C (8n-1)
D (7n+5)
Explanation opens after your attempt
Step 1
Concept
From (7d=63), (d=9) and \(a_1=2\), so \(a_n=9n-7\). From two given terms, find the common difference first.
Step 2
Why this answer is correct
The correct answer is B. (9n-7). From (7d=63), (d=9) and \(a_1=2\), so \(a_n=9n-7\). From two given terms, find the common difference first.
Step 3
Exam Tip
(7d=63) से (d=9) और \(a_1=2\), इसलिए \(a_n=9n-7\)। दो दिए पदों से पहले सामान्य अंतर निकालें।
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श्रेणी \(9,26,51,84,125,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(9,26,51,84,125,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(3n^2+6n\)
B \(4n^2+5n\)
C \(4n^2+4n+1\)
D \(5n^2+4n\)
Explanation opens after your attempt
Correct Answer
B. \(4n^2+5n\)
Step 1
Concept
The terms match \(4n^2+5n\). In a quadratic pattern, test the options on the first three terms.
Step 2
Why this answer is correct
The correct answer is B. \(4n^2+5n\). The terms match \(4n^2+5n\). In a quadratic pattern, test the options on the first three terms.
Step 3
Exam Tip
पद \(4n^2+5n\) से मिलते हैं। द्विघात पैटर्न में विकल्पों को पहले तीन पदों पर जांचें।
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यदि \(a_n=11n-15\), तो \(a_{2r-1}\) किसके बराबर होगा?
If \(a_n=11n-15\), what is \(a_{2r-1}\)?
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#nth-term
#algebra
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A (22r-26)
B (22r-15)
C (11r-26)
D (22r-4)
Explanation opens after your attempt
Correct Answer
A. (22r-26)
Step 1
Concept
Putting (n=2r-1), (a_{2r-1}=11(2r-1)-15=22r-26). Substitute the whole expression used as the index.
Step 2
Why this answer is correct
The correct answer is A. (22r-26). Putting (n=2r-1), (a_{2r-1}=11(2r-1)-15=22r-26). Substitute the whole expression used as the index.
Step 3
Exam Tip
(n=2r-1) रखने पर (a_{2r-1}=11(2r-1)-15=22r-26)। सूचकांक का पूरा व्यंजक प्रतिस्थापित करें।
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श्रेणी \(6,30,150,750,\ldots\) का (6)वां पद क्या होगा?
What is the (6)th term of the sequence \(6,30,150,750,\ldots\)?
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#progressions
#nth-term
#geometric
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A (18750)
B (15625)
C (3750)
D (12500)
Explanation opens after your attempt
Correct Answer
A. (18750)
Step 1
Concept
This is a geometric sequence and \(a_6=6\cdot5^5=18750\). In a geometric sequence, the exponent is (n-1).
Step 2
Why this answer is correct
The correct answer is A. (18750). This is a geometric sequence and \(a_6=6\cdot5^5=18750\). In a geometric sequence, the exponent is (n-1).
Step 3
Exam Tip
यह गुणोत्तर श्रेणी है और \(a_6=6\cdot5^5=18750\)। गुणोत्तर श्रेणी में घात (n-1) होती है।
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यदि \(a_n=2n^2+9n-11\), तो \(a_{10}-a_4\) का मान क्या है?
If \(a_n=2n^2+9n-11\), what is the value of \(a_{10}-a_4\)?
#sequences
#progressions
#nth-term
#quadratic
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A (198)
B (204)
C (216)
D (222)
Explanation opens after your attempt
Step 1
Concept
\(a_{10}=279\) and \(a_4=75\), so the difference is (204). Find both terms separately before subtracting.
Step 2
Why this answer is correct
The correct answer is B. (204). \(a_{10}=279\) and \(a_4=75\), so the difference is (204). Find both terms separately before subtracting.
Step 3
Exam Tip
\(a_{10}=279\) और \(a_4=75\), इसलिए अंतर (204) है। दोनों पद अलग निकालकर घटाएं।
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श्रेणी \(5,17,37,65,101,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(5,17,37,65,101,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(4n^2+1\)
B \(3n^2+2n\)
C \(4n^2+n\)
D \(2n^2+5n-2\)
Explanation opens after your attempt
Correct Answer
A. \(4n^2+1\)
Step 1
Concept
The second differences are (8), and \(4n^2+1\) gives all starting terms. Half of the second difference is the coefficient of \(n^2\).
Step 2
Why this answer is correct
The correct answer is A. \(4n^2+1\). The second differences are (8), and \(4n^2+1\) gives all starting terms. Half of the second difference is the coefficient of \(n^2\).
Step 3
Exam Tip
दूसरे अंतर (8) हैं और \(4n^2+1\) सभी शुरुआती पद देता है। दूसरे अंतर का आधा \(n^2\) का गुणांक होता है।
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यदि \(a_n=35-6n\), तो कौन सा पद (-43) के बराबर है?
If \(a_n=35-6n\), which term is equal to (-43)?
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#nth-term
#equation
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A (12)वां / (12)th
B (13)वां / (13)th
C (14)वां / (14)th
D (15)वां / (15)th
Explanation opens after your attempt
Correct Answer
B. (13)वां / (13)th
Step 1
Concept
From (35-6n=-43), (6n=78), so (n=13). Be careful with signs in negative terms.
Step 2
Why this answer is correct
The correct answer is B. (13)वां / (13)th. From (35-6n=-43), (6n=78), so (n=13). Be careful with signs in negative terms.
Step 3
Exam Tip
(35-6n=-43) से (6n=78), इसलिए (n=13)। ऋणात्मक पदों में चिन्हों पर ध्यान दें।
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श्रेणी \(8,21,40,65,96,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(8,21,40,65,96,\ldots\)?
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#nth-term
#quadratic
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A \(2n^2+5n+1\)
B \(n^2+10n-3\)
C \(3n^2+4n+1\)
D \(3n^2+5n\)
Explanation opens after your attempt
Correct Answer
C. \(3n^2+4n+1\)
Step 1
Concept
The given terms match \(3n^2+4n+1\). Testing options on the first three terms is a safe method.
Step 2
Why this answer is correct
The correct answer is C. \(3n^2+4n+1\). The given terms match \(3n^2+4n+1\). Testing options on the first three terms is a safe method.
Step 3
Exam Tip
दिए गए पद \(3n^2+4n+1\) से मिलते हैं। विकल्पों को पहले तीन पदों पर जांचना सुरक्षित तरीका है।
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यदि (a_n=(-1)^n(5n-3)), तो \(a_9\) का मान क्या होगा?
If (a_n=(-1)^n(5n-3)), what is the value of \(a_9\)?
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#nth-term
#alternating
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A (42)
B (-42)
C (48)
D (-48)
Explanation opens after your attempt
Step 1
Concept
For (n=9), ((-1)9 =-1) and (5(9)-3=42), so \(a_9=-42\). In alternating signs, check the even-odd position.
Step 2
Why this answer is correct
The correct answer is B. (-42). For (n=9), ((-1)9 =-1) and (5(9)-3=42), so \(a_9=-42\). In alternating signs, check the even-odd position.
Step 3
Exam Tip
(n=9) पर ((-1)9 =-1) और (5(9)-3=42), इसलिए \(a_9=-42\)। वैकल्पिक चिन्ह में सम-विषम स्थिति देखें।
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किसी समान्तर श्रेणी में \(a_9=61\) और सामान्य अंतर (7) है। उसका (n)वां पद क्या होगा?
In an arithmetic sequence, \(a_9=61\) and the common difference is (7). What is its (n)th term?
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#progressions
#nth-term
#arithmetic
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A (7n-2)
B (7n+5)
C (7n+12)
D (9n-20)
Explanation opens after your attempt
Step 1
Concept
From \(a_9=a_1+8d\), \(a_1=5\), so (a_n=5+(n-1)7=7n-2). Finding the first term from a middle term is useful.
Step 2
Why this answer is correct
The correct answer is A. (7n-2). From \(a_9=a_1+8d\), \(a_1=5\), so (a_n=5+(n-1)7=7n-2). Finding the first term from a middle term is useful.
Step 3
Exam Tip
\(a_9=a_1+8d\) से \(a_1=5\), इसलिए (a_n=5+(n-1)7=7n-2)। मध्य पद से पहला पद निकालना उपयोगी है।
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श्रेणी \(13,29,61,125,253,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(13,29,61,125,253,\ldots\)?
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#progressions
#nth-term
#exponential
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A \(2^{n+2}+5\)
B \(2^{n+3}-3\)
C \(2^{n+1}+9\)
D (4n+9)
Explanation opens after your attempt
Correct Answer
B. \(2^{n+3}-3\)
Step 1
Concept
The terms are \(16-3,32-3,64-3,\ldots\), so \(a_n=2^{n+3}-3\). In exponential patterns, identify the starting power.
Step 2
Why this answer is correct
The correct answer is B. \(2^{n+3}-3\). The terms are \(16-3,32-3,64-3,\ldots\), so \(a_n=2^{n+3}-3\). In exponential patterns, identify the starting power.
Step 3
Exam Tip
पद \(16-3,32-3,64-3,\ldots\) हैं इसलिए \(a_n=2^{n+3}-3\)। घातीय पैटर्न में शुरुआती घात पहचानें।
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श्रेणी \(\frac{11}{6},\frac{11}{3},\frac{11}{2},\frac{22}{3},\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(\frac{11}{6},\frac{11}{3},\frac{11}{2},\frac{22}{3},\ldots\)?
#sequences
#progressions
#nth-term
#fractions
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A \(\frac{11n}{6}\)
B (\frac{11(n+1)}{6})
C \(\frac{6n}{11}\)
D (11n)
Explanation opens after your attempt
Correct Answer
A. \(\frac{11n}{6}\)
Step 1
Concept
Each term increases by \(\frac{11}{6}\), so \(a_n=\frac{11n}{6}\). Use a common denominator to see the pattern in fractions.
Step 2
Why this answer is correct
The correct answer is A. \(\frac{11n}{6}\). Each term increases by \(\frac{11}{6}\), so \(a_n=\frac{11n}{6}\). Use a common denominator to see the pattern in fractions.
Step 3
Exam Tip
हर पद में \(\frac{11}{6}\) की वृद्धि है इसलिए \(a_n=\frac{11n}{6}\)। भिन्नों में समान हर बनाकर पैटर्न देखें।
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श्रेणी \(6,19,42,75,118,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(6,19,42,75,118,\ldots\)?
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#progressions
#nth-term
#quadratic
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A \(4n^2+n+1\)
B \(5n^2-1\)
C \(3n^2+4n-1\)
D \(5n^2+2n-1\)
Explanation opens after your attempt
Correct Answer
B. \(5n^2-1\)
Step 1
Concept
The terms match \(5n^2+1\), so none of the listed options is correct. Always test options on the first term.
Step 2
Why this answer is correct
The correct answer is B. \(5n^2-1\). The terms match \(5n^2+1\), so none of the listed options is correct. Always test options on the first term.
Step 3
Exam Tip
पद \(5n^2+1\) नहीं बल्कि \(5n^2+1\) से मिलते हैं, इसलिए दिए विकल्पों में सही पद नहीं है। सही विकल्पों को पहले पद पर अवश्य जांचें।
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यदि \(a_n=8n^2-7n+4\), तो \(a_{n+1}-a_n\) क्या होगा?
If \(a_n=8n^2-7n+4\), what is \(a_{n+1}-a_n\)?
#sequences
#progressions
#nth-term
#algebra
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A (16n+1)
B (16n-7)
C (8n+1)
D (16n+9)
Explanation opens after your attempt
Correct Answer
A. (16n+1)
Step 1
Concept
\(a_{n+1}=8n^2+9n+5\), so the difference is (16n+1). Expand ((n+1)2 ) carefully.
Step 2
Why this answer is correct
The correct answer is A. (16n+1). \(a_{n+1}=8n^2+9n+5\), so the difference is (16n+1). Expand ((n+1)2 ) carefully.
Step 3
Exam Tip
\(a_{n+1}=8n^2+9n+5\), इसलिए अंतर (16n+1) है। (n+1) का वर्ग सावधानी से खोलें।
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किसी श्रेणी का \(a_n=2n^3-3n\) है। \(a_5\) का मान क्या है?
A sequence has \(a_n=2n^3-3n\). What is the value of \(a_5\)?
#sequences
#progressions
#nth-term
#cubic
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A (225)
B (235)
C (245)
D (250)
Explanation opens after your attempt
Step 1
Concept
(a_5=2(5)3 -3(5)=235). Calculate the cubic and linear parts separately.
Step 2
Why this answer is correct
The correct answer is B. (235). (a_5=2(5)3 -3(5)=235). Calculate the cubic and linear parts separately.
Step 3
Exam Tip
(a_5=2(5)3 -3(5)=235)। घन और रैखिक भाग अलग-अलग निकालें।
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श्रेणी \(44,37,30,23,16,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(44,37,30,23,16,\ldots\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (51-7n)
B (44-7n)
C (7n+37)
D (50-6n)
Explanation opens after your attempt
Correct Answer
A. (51-7n)
Step 1
Concept
The first term is (44) and the difference is (-7), so (a_n=44+(n-1)(-7)=51-7n). Use a negative difference in a decreasing sequence.
Step 2
Why this answer is correct
The correct answer is A. (51-7n). The first term is (44) and the difference is (-7), so (a_n=44+(n-1)(-7)=51-7n). Use a negative difference in a decreasing sequence.
Step 3
Exam Tip
पहला पद (44) और अंतर (-7) है, इसलिए (a_n=44+(n-1)(-7)=51-7n)। घटती श्रेणी में अंतर ऋणात्मक लें।
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यदि \(a_n=4^n-3n\), तो \(a_4\) का मान क्या होगा?
If \(a_n=4^n-3n\), what is the value of \(a_4\)?
#sequences
#progressions
#nth-term
#exponential
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A (240)
B (244)
C (248)
D (252)
Explanation opens after your attempt
Step 1
Concept
(a_4=44 -3(4)=256-12=244). Calculate the power and the linear part separately.
Step 2
Why this answer is correct
The correct answer is B. (244). (a_4=44 -3(4)=256-12=244). Calculate the power and the linear part separately.
Step 3
Exam Tip
(a_4=44 -3(4)=256-12=244)। घात और रैखिक भाग अलग निकालें।
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श्रेणी \(18,34,54,78,106,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(18,34,54,78,106,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(2n^2+10n+6\)
B \(3n^2+7n+8\)
C \(n^2+13n+4\)
D \(2n^2+12n+4\)
Explanation opens after your attempt
Correct Answer
A. \(2n^2+10n+6\)
Step 1
Concept
The second differences are (4), and \(2n^2+10n+6\) gives the starting terms. Confirm a quadratic rule using the first three terms.
Step 2
Why this answer is correct
The correct answer is A. \(2n^2+10n+6\). The second differences are (4), and \(2n^2+10n+6\) gives the starting terms. Confirm a quadratic rule using the first three terms.
Step 3
Exam Tip
दूसरे अंतर (4) हैं और \(2n^2+10n+6\) शुरुआती पद देता है। द्विघात नियम में पहले तीन पदों से पुष्टि करें।
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किसी समान्तर श्रेणी का (n)वां पद \(a_n=13n-19\) है। कौन सा पद (176) है?
The (n)th term of an arithmetic sequence is \(a_n=13n-19\). Which term is (176)?
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#nth-term
#equation
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A (13)वां / (13)th
B (14)वां / (14)th
C (15)वां / (15)th
D (16)वां / (16)th
Explanation opens after your attempt
Correct Answer
C. (15)वां / (15)th
Step 1
Concept
From (13n-19=176), (13n=195), 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 (13n-19=176), (13n=195), so (n=15). Form an equation to find the term number.
Step 3
Exam Tip
(13n-19=176) से (13n=195), इसलिए (n=15)। पद संख्या निकालने के लिए समीकरण बनाएं।
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श्रेणी \(\frac{13}{7},\frac{26}{7},\frac{39}{7},\frac{52}{7},\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(\frac{13}{7},\frac{26}{7},\frac{39}{7},\frac{52}{7},\ldots\)?
#sequences
#progressions
#nth-term
#fractions
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A \(\frac{7n}{13}\)
B (\frac{13(n+1)}{7})
C \(\frac{13n}{7}\)
D (13n)
Explanation opens after your attempt
Correct Answer
C. \(\frac{13n}{7}\)
Step 1
Concept
Each term increases by \(\frac{13}{7}\), so \(a_n=\frac{13n}{7}\). In fractions with a common denominator, observe the numerator pattern.
Step 2
Why this answer is correct
The correct answer is C. \(\frac{13n}{7}\). Each term increases by \(\frac{13}{7}\), so \(a_n=\frac{13n}{7}\). In fractions with a common denominator, observe the numerator pattern.
Step 3
Exam Tip
हर पद में \(\frac{13}{7}\) की वृद्धि है इसलिए \(a_n=\frac{13n}{7}\)। समान हर वाले भिन्नों में अंश का पैटर्न देखें।
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यदि \(a_n=3n^2+5n-8\), तो \(a_9-a_6\) का मान क्या है?
If \(a_n=3n^2+5n-8\), what is the value of \(a_9-a_6\)?
#sequences
#progressions
#nth-term
#quadratic
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A (120)
B (126)
C (132)
D (138)
Explanation opens after your attempt
Step 1
Concept
\(a_9=280\) and \(a_6=160\), so the difference is (120). Find both terms separately before subtracting.
Step 2
Why this answer is correct
The correct answer is A. (120). \(a_9=280\) and \(a_6=160\), so the difference is (120). Find both terms separately before subtracting.
Step 3
Exam Tip
\(a_9=280\) और \(a_6=160\), इसलिए अंतर (120) है। दोनों पद अलग निकालकर घटाएं।
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श्रेणी \(7,28,63,112,175,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(7,28,63,112,175,\ldots\)?
#sequences
#progressions
#nth-term
#squares
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A \(7n^2\)
B (7n+7)
C \(n^2+6n\)
D \(7n^2+7\)
Explanation opens after your attempt
Correct Answer
A. \(7n^2\)
Step 1
Concept
The terms are \(7\cdot1^2,7\cdot2^2,7\cdot3^2,\ldots\), so \(a_n=7n^2\). Identify the coefficient of the square pattern.
Step 2
Why this answer is correct
The correct answer is A. \(7n^2\). The terms are \(7\cdot1^2,7\cdot2^2,7\cdot3^2,\ldots\), so \(a_n=7n^2\). Identify the coefficient of the square pattern.
Step 3
Exam Tip
पद \(7\cdot1^2,7\cdot2^2,7\cdot3^2,\ldots\) हैं इसलिए \(a_n=7n^2\)। वर्ग पैटर्न के गुणांक को पहचानें।
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यदि \(a_n=28-5n\), तो \(a_7+a_{12}\) का मान क्या है?
If \(a_n=28-5n\), what is the value of \(a_7+a_{12}\)?
#sequences
#progressions
#nth-term
#linear
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A (-37)
B (-39)
C (-41)
D (-43)
Explanation opens after your attempt
Step 1
Concept
\(a_7=-7\) and \(a_{12}=-32\), so the sum is (-39). Add negative numbers carefully.
Step 2
Why this answer is correct
The correct answer is B. (-39). \(a_7=-7\) and \(a_{12}=-32\), so the sum is (-39). Add negative numbers carefully.
Step 3
Exam Tip
\(a_7=-7\) और \(a_{12}=-32\), इसलिए योग (-39) है। ऋणात्मक संख्याओं का योग सावधानी से करें।
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श्रेणी \(64,125,216,343,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(64,125,216,343,\ldots\)?
#sequences
#progressions
#nth-term
#cubes
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A \(n^3+63\)
B ((n+2)3 )
C ((n+3)3 )
D \(4n^3\)
Explanation opens after your attempt
Correct Answer
C. ((n+3)3 )
Step 1
Concept
The terms are \(4^3,5^3,6^3,\ldots\), so (a_n=(n+3)3 ). In cube sequences, observe the starting base.
Step 2
Why this answer is correct
The correct answer is C. ((n+3)3 ). The terms are \(4^3,5^3,6^3,\ldots\), so (a_n=(n+3)3 ). In cube sequences, observe the starting base.
Step 3
Exam Tip
पद \(4^3,5^3,6^3,\ldots\) हैं इसलिए (a_n=(n+3)3 )। घन श्रेणी में शुरुआती आधार देखें।
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किसी श्रेणी का \(a_n=10n-7\) है। \(a_{n+6}-a_n\) का मान क्या होगा?
A sequence has \(a_n=10n-7\). What is the value of \(a_{n+6}-a_n\)?
#sequences
#progressions
#nth-term
#difference
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A (40)
B (50)
C (60)
D (70)
Explanation opens after your attempt
Step 1
Concept
The index increases by (6) and the common difference is (10), so the difference is (60). In a linear rule, the coefficient of (n) gives the common difference.
Step 2
Why this answer is correct
The correct answer is C. (60). The index increases by (6) and the common difference is (10), so the difference is (60). In a linear rule, the coefficient of (n) gives the common difference.
Step 3
Exam Tip
सूचकांक (6) बढ़ा है और सामान्य अंतर (10) है इसलिए अंतर (60) होगा। रैखिक नियम में (n) का गुणांक सामान्य अंतर देता है।
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श्रेणी \(8,24,72,216,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(8,24,72,216,\ldots\)?
#sequences
#progressions
#nth-term
#geometric
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A \(8\cdot3^{n-1}\)
B \(3\cdot8^{n-1}\)
C \(8\cdot3^n\)
D \(24\cdot3^{n-1}\)
Explanation opens after your attempt
Correct Answer
A. \(8\cdot3^{n-1}\)
Step 1
Concept
Each term is multiplied by (3), so \(a_n=8\cdot3^{n-1}\). In a geometric sequence, the first term stays separate.
Step 2
Why this answer is correct
The correct answer is A. \(8\cdot3^{n-1}\). Each term is multiplied by (3), so \(a_n=8\cdot3^{n-1}\). In a geometric sequence, the first term stays separate.
Step 3
Exam Tip
हर बार गुणन (3) हो रहा है इसलिए \(a_n=8\cdot3^{n-1}\)। गुणोत्तर श्रेणी में पहला पद अलग रहता है।
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यदि \(a_n=5n^2+2n-9\), तो \(a_{n+2}-a_n\) क्या होगा?
If \(a_n=5n^2+2n-9\), what is \(a_{n+2}-a_n\)?
#sequences
#progressions
#nth-term
#algebra
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A (20n+24)
B (20n+22)
C (10n+14)
D (20n+18)
Explanation opens after your attempt
Correct Answer
A. (20n+24)
Step 1
Concept
\(a_{n+2}=5n^2+22n+15\), so the difference is (20n+24). Expand ((n+2)2 ) correctly.
Step 2
Why this answer is correct
The correct answer is A. (20n+24). \(a_{n+2}=5n^2+22n+15\), so the difference is (20n+24). Expand ((n+2)2 ) correctly.
Step 3
Exam Tip
\(a_{n+2}=5n^2+22n+15\), इसलिए अंतर (20n+24) है। (n+2) का वर्ग सही खोलें।
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किसी समान्तर श्रेणी में \(a_8=73\) और \(a_{17}=181\) है। \(a_{26}\) क्या होगा?
In an arithmetic sequence, \(a_8=73\) and \(a_{17}=181\). What is \(a_{26}\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (285)
B (289)
C (293)
D (297)
Explanation opens after your attempt
Step 1
Concept
From (9d=108), (d=12), so \(a_{26}=181+9\cdot12=289\). It is easier to find a distant term from a nearby given term.
Step 2
Why this answer is correct
The correct answer is B. (289). From (9d=108), (d=12), so \(a_{26}=181+9\cdot12=289\). It is easier to find a distant term from a nearby given term.
Step 3
Exam Tip
(9d=108) से (d=12), इसलिए \(a_{26}=181+9\cdot12=289\)। निकट दिए गए पद से दूर का पद निकालना आसान है।
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श्रेणी \(2,12,30,56,90,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(2,12,30,56,90,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(4n^2-2n\)
B \(3n^2-n\)
C \(2n^2+2n-2\)
D \(5n^2-3n\)
Explanation opens after your attempt
Correct Answer
A. \(4n^2-2n\)
Step 1
Concept
The given terms match \(4n^2-2n\). Testing options on the first three terms reduces mistakes.
Step 2
Why this answer is correct
The correct answer is A. \(4n^2-2n\). The given terms match \(4n^2-2n\). Testing options on the first three terms reduces mistakes.
Step 3
Exam Tip
दिए गए पद \(4n^2-2n\) से मिलते हैं। पहले तीन पदों पर विकल्प जांचने से गलती कम होती है।
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यदि \(a_n=7n-13\), तो \(a_{4n+1}\) क्या होगा?
If \(a_n=7n-13\), what is \(a_{4n+1}\)?
#sequences
#progressions
#nth-term
#algebra
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A (28n-6)
B (28n-13)
C (28n+7)
D (7n-6)
Explanation opens after your attempt
Correct Answer
A. (28n-6)
Step 1
Concept
Replacing (n) by (4n+1), (7(4n+1)-13=28n-6). Put the whole index in brackets while solving.
Step 2
Why this answer is correct
The correct answer is A. (28n-6). Replacing (n) by (4n+1), (7(4n+1)-13=28n-6). Put the whole index in brackets while solving.
Step 3
Exam Tip
(n) की जगह (4n+1) रखने पर (7(4n+1)-13=28n-6)। पूरे सूचकांक को ब्रैकेट में रखकर हल करें।
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श्रेणी \(23,38,53,68,\ldots\) में (218) कौन सा पद है?
In the sequence \(23,38,53,68,\ldots\), which term is (218)?
#sequences
#progressions
#nth-term
#arithmetic
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A (12)वां / (12)th
B (13)वां / (13)th
C (14)वां / (14)th
D (15)वां / (15)th
Explanation opens after your attempt
Correct Answer
C. (14)वां / (14)th
Step 1
Concept
From (23+(n-1)15=218), (n-1=13), so (n=14). Do not forget (n-1) while finding the term number.
Step 2
Why this answer is correct
The correct answer is C. (14)वां / (14)th. From (23+(n-1)15=218), (n-1=13), so (n=14). Do not forget (n-1) while finding the term number.
Step 3
Exam Tip
(23+(n-1)15=218) से (n-1=13), इसलिए (n=14)। पद संख्या निकालते समय (n-1) को न भूलें।
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यदि (a_n=\frac{n(n+7)}{4}), तो \(a_{12}\) का मान क्या होगा?
If (a_n=\frac{n(n+7)}{4}), what is the value of \(a_{12}\)?
#sequences
#progressions
#nth-term
#formula
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A (54)
B (57)
C (60)
D (63)
Explanation opens after your attempt
Step 1
Concept
(a_{12}=\frac{12(19)}{4}=57). Simplifying first makes fraction calculation easier.
Step 2
Why this answer is correct
The correct answer is B. (57). (a_{12}=\frac{12(19)}{4}=57). Simplifying first makes fraction calculation easier.
Step 3
Exam Tip
(a_{12}=\frac{12(19)}{4}=57)। भिन्न में पहले सरल करना गणना आसान बनाता है।
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श्रेणी \(11,31,59,95,139,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(11,31,59,95,139,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(4n^2+8n-1\)
B \(3n^2+11n-3\)
C \(5n^2+5n+1\)
D \(4n^2+9n-2\)
Explanation opens after your attempt
Correct Answer
A. \(4n^2+8n-1\)
Step 1
Concept
The second differences are (8), and \(4n^2+8n-1\) 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 A. \(4n^2+8n-1\). The second differences are (8), and \(4n^2+8n-1\) gives all starting terms. In a quadratic sequence, test options on the first three terms.
Step 3
Exam Tip
दूसरे अंतर (8) हैं और \(4n^2+8n-1\) सभी शुरुआती पद देता है। द्विघात श्रेणी में विकल्पों को पहले तीन पदों पर जांचें।
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यदि \(a_n=9\cdot2^{n-1}+4\), तो \(a_6\) का मान क्या होगा?
If \(a_n=9\cdot2^{n-1}+4\), what is the value of \(a_6\)?
#sequences
#progressions
#nth-term
#exponential
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A (286)
B (290)
C (292)
D (296)
Explanation opens after your attempt
Step 1
Concept
\(a_6=9\cdot2^5+4=292\). Keep the exponent (n-1) correctly.
Step 2
Why this answer is correct
The correct answer is C. (292). \(a_6=9\cdot2^5+4=292\). Keep the exponent (n-1) correctly.
Step 3
Exam Tip
\(a_6=9\cdot2^5+4=292\)। (n-1) वाली घात को सही रखें।
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श्रेणी \(-4,8,-12,16,-20,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(-4,8,-12,16,-20,\ldots\)?
#sequences
#progressions
#nth-term
#alternating
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A (4(-1)^{n+1}n)
B (4(-1)^n n)
C (4n)
D ((-1)^n n)
Explanation opens after your attempt
Correct Answer
B. (4(-1)^n n)
Step 1
Concept
For odd (n), terms are negative and for even (n), terms are positive, so (a_n=4(-1)^n n). In alternating signs, test first at (n=1).
Step 2
Why this answer is correct
The correct answer is B. (4(-1)^n n). For odd (n), terms are negative and for even (n), terms are positive, so (a_n=4(-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=4(-1)^n n)। वैकल्पिक चिन्ह में पहले (n=1) पर जांचें।
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यदि \(a_n=n^2+14\), तो कौन सा पद (183) है?
If \(a_n=n^2+14\), which term is (183)?
#sequences
#progressions
#nth-term
#term-number
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A (11)वां / (11)th
B (12)वां / (12)th
C (13)वां / (13)th
D कोई पूर्णांक पद नहीं / No integral term
Explanation opens after your attempt
Correct Answer
C. (13)वां / (13)th
Step 1
Concept
From \(n^2+14=183\), \(n^2=169\), so (n=13). A term number is taken as a positive integer.
Step 2
Why this answer is correct
The correct answer is C. (13)वां / (13)th. From \(n^2+14=183\), \(n^2=169\), so (n=13). A term number is taken as a positive integer.
Step 3
Exam Tip
\(n^2+14=183\) से \(n^2=169\), इसलिए (n=13)। पद संख्या धन पूर्णांक ही ली जाती है।
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श्रेणी \(48,24,12,6,3,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(48,24,12,6,3,\ldots\)?
#sequences
#progressions
#nth-term
#geometric
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A (48\left\(\frac{1}{2}\right\)^n)
B (24\left\(\frac{1}{2}\right\)^{n-1})
C (48\left\(\frac{1}{2}\right\)^{n-1})
D \(\frac{48}{n}\)
Explanation opens after your attempt
Correct Answer
C. (48\left\(\frac{1}{2}\right\)^{n-1})
Step 1
Concept
Each term is halved, so (a_n=48\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. (48\left\(\frac{1}{2}\right\)^{n-1}). Each term is halved, so (a_n=48\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=48\left\(\frac{1}{2}\right\)^{n-1})। गुणोत्तर श्रेणी में घात (n-1) से शुरू होती है।
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किसी श्रेणी का \(a_n=6n^2-11n+9\) है। \(a_{11}-a_5\) का मान क्या है?
A sequence has \(a_n=6n^2-11n+9\). What is the value of \(a_{11}-a_5\)?
#sequences
#progressions
#nth-term
#quadratic
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A (540)
B (546)
C (552)
D (558)
Explanation opens after your attempt
Step 1
Concept
\(a_{11}=614\) and \(a_5=74\), so the difference is (540). Find both terms separately and subtract.
Step 2
Why this answer is correct
The correct answer is A. (540). \(a_{11}=614\) and \(a_5=74\), so the difference is (540). Find both terms separately and subtract.
Step 3
Exam Tip
\(a_{11}=614\) और \(a_5=74\), इसलिए अंतर (540) है। दोनों पद अलग-अलग निकालकर घटाएं।
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श्रेणी \(27,49,71,93,\ldots\) का (20)वां पद क्या होगा?
What is the (20)th term of the sequence \(27,49,71,93,\ldots\)?
#sequences
#progressions
#nth-term
#arithmetic
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A (435)
B (445)
C (455)
D (465)
Explanation opens after your attempt
Step 1
Concept
The first term is (27) and the difference is (22), so \(a_{20}=27+19\cdot22=445\). The (20)th term includes (19) differences.
Step 2
Why this answer is correct
The correct answer is B. (445). The first term is (27) and the difference is (22), so \(a_{20}=27+19\cdot22=445\). The (20)th term includes (19) differences.
Step 3
Exam Tip
पहला पद (27) और अंतर (22) है, इसलिए \(a_{20}=27+19\cdot22=445\)। (20)वें पद में (19) अंतर जुड़ते हैं।
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यदि \(a_n=4n^2+7n\), तो \(a_8-a_3\) का मान क्या है?
If \(a_n=4n^2+7n\), what is the value of \(a_8-a_3\)?
#sequences
#progressions
#nth-term
#quadratic
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A (245)
B (255)
C (265)
D (275)
Explanation opens after your attempt
Step 1
Concept
\(a_8=312\) and \(a_3=57\), so the difference is (255). Recheck the calculation before matching options.
Step 2
Why this answer is correct
The correct answer is C. (265). \(a_8=312\) and \(a_3=57\), so the difference is (255). Recheck the calculation before matching options.
Step 3
Exam Tip
\(a_8=312\) और \(a_3=57\), इसलिए अंतर (255) है। विकल्प मिलाने से पहले गणना दोबारा जांचें।
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श्रेणी \(9,36,81,144,225,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(9,36,81,144,225,\ldots\)?
#sequences
#progressions
#nth-term
#squares
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A \(9n^2\)
B \(3n^2\)
C \(n^2+8n\)
D \(9n^2+9\)
Explanation opens after your attempt
Correct Answer
A. \(9n^2\)
Step 1
Concept
The terms are \(9\cdot1^2,9\cdot2^2,9\cdot3^2,\ldots\), so \(a_n=9n^2\). Identify the coefficient of the square pattern.
Step 2
Why this answer is correct
The correct answer is A. \(9n^2\). The terms are \(9\cdot1^2,9\cdot2^2,9\cdot3^2,\ldots\), so \(a_n=9n^2\). Identify the coefficient of the square pattern.
Step 3
Exam Tip
पद \(9\cdot1^2,9\cdot2^2,9\cdot3^2,\ldots\) हैं इसलिए \(a_n=9n^2\)। वर्ग पैटर्न के गुणांक को पहचानें।
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यदि \(a_n=55-8n\), तो \(a_n=7\) कब होगा?
If \(a_n=55-8n\), when will \(a_n=7\)?
#sequences
#progressions
#nth-term
#equation
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A (5)वां / (5)th
B (6)वां / (6)th
C (7)वां / (7)th
D (8)वां / (8)th
Explanation opens after your attempt
Correct Answer
B. (6)वां / (6)th
Step 1
Concept
From (55-8n=7), (8n=48), so (n=6). Form an equation to find the term number.
Step 2
Why this answer is correct
The correct answer is B. (6)वां / (6)th. From (55-8n=7), (8n=48), so (n=6). Form an equation to find the term number.
Step 3
Exam Tip
(55-8n=7) से (8n=48), इसलिए (n=6)। समीकरण बनाकर पद संख्या निकालें।
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श्रेणी \(16,43,82,133,196,\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(16,43,82,133,196,\ldots\)?
#sequences
#progressions
#nth-term
#quadratic
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A \(6n^2+9n+1\)
B \(5n^2+11n\)
C \(7n^2+4n+5\)
D \(6n^2+8n+2\)
Explanation opens after your attempt
Correct Answer
A. \(6n^2+9n+1\)
Step 1
Concept
The second differences are (12), and \(6n^2+9n+1\) gives all starting terms. In a quadratic rule, half of the second difference is the coefficient of \(n^2\).
Step 2
Why this answer is correct
The correct answer is A. \(6n^2+9n+1\). The second differences are (12), and \(6n^2+9n+1\) gives all starting terms. In a quadratic rule, half of the second difference is the coefficient of \(n^2\).
Step 3
Exam Tip
दूसरे अंतर (12) हैं और \(6n^2+9n+1\) सभी शुरुआती पद देता है। द्विघात नियम में दूसरे अंतर का आधा \(n^2\) का गुणांक होता है।
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यदि \(a_n=6n+17\), तो \(a_{5p-3}\) क्या होगा?
If \(a_n=6n+17\), what is \(a_{5p-3}\)?
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#progressions
#nth-term
#algebra
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A (30p-1)
B (30p+17)
C (30p-18)
D (6p-1)
Explanation opens after your attempt
Correct Answer
A. (30p-1)
Step 1
Concept
Putting (n=5p-3), (6(5p-3)+17=30p-1). Substitute the whole expression given in the index.
Step 2
Why this answer is correct
The correct answer is A. (30p-1). Putting (n=5p-3), (6(5p-3)+17=30p-1). Substitute the whole expression given in the index.
Step 3
Exam Tip
(n=5p-3) रखने पर (6(5p-3)+17=30p-1)। सूचकांक में दिया पूरा व्यंजक प्रतिस्थापित करें।
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श्रेणी \(7,11,19,35,67,\ldots\) का (n)वां पद कौन सा है?
Which is the (n)th term of the sequence \(7,11,19,35,67,\ldots\)?
#sequences
#progressions
#nth-term
#exponential
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A \(2^n+5\)
B \(2^{n+1}+3\)
C \(2^n+n+4\)
D (4n+3)
Explanation opens after your attempt
Correct Answer
A. \(2^n+5\)
Step 1
Concept
The terms match \(2^n+5\). Test the rule on several starting terms.
Step 2
Why this answer is correct
The correct answer is A. \(2^n+5\). The terms match \(2^n+5\). Test the rule on several starting terms.
Step 3
Exam Tip
पद (2+5,4+7) नहीं बल्कि \(2^n+5\) से मिलते हैं। पहले कई पदों पर नियम जांचें।
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यदि (a_n=n(n+6)), तो कौन सा पद (160) है?
If (a_n=n(n+6)), which term is (160)?
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#progressions
#nth-term
#equation
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A (8)वां / (8)th
B (9)वां / (9)th
C (10)वां / (10)th
D (11)वां / (11)th
Explanation opens after your attempt
Correct Answer
C. (10)वां / (10)th
Step 1
Concept
Putting (n=10), (10(10+6)=160). Directly testing the options can be a quick method.
Step 2
Why this answer is correct
The correct answer is C. (10)वां / (10)th. Putting (n=10), (10(10+6)=160). Directly testing the options can be a quick method.
Step 3
Exam Tip
(n=10) रखने पर (10(10+6)=160)। विकल्पों को सीधे जांचना तेज तरीका हो सकता है।
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किसी समान्तर श्रेणी का (n)वां पद \(a_n=15n-23\) है। सामान्य अंतर क्या है?
The (n)th term of an arithmetic sequence is \(a_n=15n-23\). What is the common difference?
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#common-difference
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A (8)
B (15)
C (23)
D (38)
Explanation opens after your attempt
Step 1
Concept
In \(a_n=15n-23\), the coefficient of (n) is (15), so the common difference is (15). In a linear (n)th term, the coefficient of (n) gives the difference.
Step 2
Why this answer is correct
The correct answer is B. (15). In \(a_n=15n-23\), the coefficient of (n) is (15), so the common difference is (15). In a linear (n)th term, the coefficient of (n) gives the difference.
Step 3
Exam Tip
\(a_n=15n-23\) में (n) का गुणांक (15) है, इसलिए सामान्य अंतर (15) है। रैखिक (n)वें पद में (n) का गुणांक अंतर देता है।
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श्रेणी \(125,25,5,1,\frac{1}{5},\ldots\) का (n)वां पद क्या है?
What is the (n)th term of the sequence \(125,25,5,1,\frac{1}{5},\ldots\)?
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#nth-term
#geometric
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A (125\left\(\frac{1}{5}\right\)^n)
B (25\left\(\frac{1}{5}\right\)^{n-1})
C (125\left\(\frac{1}{5}\right\)^{n-1})
D \(\frac{125}{n}\)
Explanation opens after your attempt
Correct Answer
C. (125\left\(\frac{1}{5}\right\)^{n-1})
Step 1
Concept
Each term is multiplied by \(\frac{1}{5}\), so (a_n=125\left\(\frac{1}{5}\right\)^{n-1}). Keep the first term fixed and use exponent (n-1).
Step 2
Why this answer is correct
The correct answer is C. (125\left\(\frac{1}{5}\right\)^{n-1}). Each term is multiplied by \(\frac{1}{5}\), so (a_n=125\left\(\frac{1}{5}\right\)^{n-1}). Keep the first term fixed and use exponent (n-1).
Step 3
Exam Tip
हर पद \(\frac{1}{5}\) गुना हो रहा है इसलिए (a_n=125\left\(\frac{1}{5}\right\)^{n-1})। पहले पद को सुरक्षित रखकर (n-1) घात लगाएं।
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