Level 49 • 21/50 questions • 25 seconds per question.
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What is the general term of the sequence \(2,11,26,47,\ldots\)?
B. \(a_n=3n^2-1\)
\(3n^2-1\) से (2,11,26,47) मिलते हैं। परीक्षा में दूसरे अंतर देखकर वर्गीय नियम पहचानें। / \(3n^2-1\) gives (2,11,26,47). In exams, identify a quadratic rule from second differences.
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Which general term is correct for the sequence \(\frac{5}{2},9,\frac{39}{2},34,\ldots\)?
A. (a_n=\frac{n(4n+1)}{2})
(\frac{n(4n+1)}{2}) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को भी छोटे (n) से जाँचें। / (\frac{n(4n+1)}{2}) gives the given terms. In exams, test fractional terms with small (n).
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What is the general term of the sequence \(139,128,117,106,\ldots\)?
B. \(a_n=150-11n\)
(n=1) पर (139) और (n=2) पर (128) मिलता है, इसलिए \(a_n=150-11n\) है। परीक्षा में घटते अनुक्रम का पहला पद मिलाएँ। / At (n=1) it gives (139), and at (n=2) it gives (128), so \(a_n=150-11n\). In exams, match the first term of a decreasing sequence.
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If \(a_n=8n-5\), which term is equal to (155)?
C. (n=20)
(8n-5=155) से (n=20) मिलता है। परीक्षा में पद संख्या के लिए सूत्र को दिए मान के बराबर रखें। / From (8n-5=155), we get (n=20). In exams, equate the formula to the given value to find the term number.
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In the sequence \(4,15,26,37,\ldots\), which term is (125)?
C. बारहवाँ पद(12)th term
इसका नियम \(a_n=11n-7\) है और (11n-7=125) से (n=12) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें। / Its rule is \(a_n=11n-7\), and (11n-7=125) gives (n=12). In exams, equate the given term to the general term.
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Which general term is correct for the sequence \(3,8,17,32,\ldots\)?
A. \(a_n=2^n+n^2\)
\(2^n+n^2\) से (3,8,17,32) मिलते हैं। परीक्षा में घात और वर्ग वाले संयुक्त नियम जाँचें। / \(2^n+n^2\) gives (3,8,17,32). In exams, check combined power-and-square rules.
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What is the general term of the sequence \(3,12,35,96,\ldots\)?
A. \(a_n=3^n+n^2-1\)
\(3^n+n^2-1\) से (3,12,35,96) मिलते हैं। परीक्षा में तेज वृद्धि में घात वाला नियम जाँचें। / \(3^n+n^2-1\) gives (3,12,35,96). In exams, check a power rule in rapid growth.
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What is the general term of the sequence \(3,20,45,78,\ldots\)?
A. \(a_n=4n^2+5n-6\)
\(4n^2+5n-6\) से (3,20,45,78) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम चुनें। / \(4n^2+5n-6\) gives (3,20,45,78). In exams, choose a quadratic rule when second differences are constant.
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Which general term is correct for the sequence \(2,18,52,110,\ldots\)?
A. \(a_n=n^3+3n^2-2\)
\(n^3+3n^2-2\) से (2,18,52,110) मिलते हैं। परीक्षा में घन आधारित विकल्पों को छोटे (n) से जाँचें। / \(n^3+3n^2-2\) gives (2,18,52,110). In exams, test cube-based options with small (n).
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What is the general term of the sequence \(4,22,66,148,\ldots\)?
A. \(a_n=2n^3+n^2+n\)
\(2n^3+n^2+n\) से (4,22,66,148) मिलते हैं। परीक्षा में संयुक्त घन नियम भी जाँचें। / \(2n^3+n^2+n\) gives (4,22,66,148). In exams, also check combined cubic rules.
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What is the general term of the sequence \(9,26,55,96,\ldots\)?
A. \(a_n=6n^2-n+4\)
\(6n^2-n+4\) से (9,26,55,96) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम देखें। / \(6n^2-n+4\) gives (9,26,55,96). In exams, check a quadratic rule when second differences are constant.
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Which general term is correct for the sequence \(2,23,124,625,\ldots\)?
A. \(a_n=5^n+n-4\)
\(5^n+n-4\) से (2,23,124,625) मिलते हैं। परीक्षा में घात वाले नियम में छोटा रैखिक भाग भी जाँचें। / \(5^n+n-4\) gives (2,23,124,625). In exams, also check the small linear part in a power rule.
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If \(a_n=13n-10\), what is the average of the first five terms?
A. (29)
पहले पाँच पद (3,16,29,42,55) हैं और औसत (29) है। परीक्षा में औसत के लिए योग को पदों की संख्या से भाग दें। / The first five terms are (3,16,29,42,55), and the average is (29). In exams, divide the sum by the number of terms.
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In the sequence \(3,16,29,42,\ldots\), which term is (159)?
B. तेरहवाँ पद(13)th term
इसका नियम \(a_n=13n-10\) है और (13n-10=159) से (n=13) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें। / Its rule is \(a_n=13n-10\), and (13n-10=159) gives (n=13). In exams, equate the given term to the general term.
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What is the general term of the sequence \(0,12,72,240,\ldots\)?
A. \(a_n=n^4-n^2\)
\(n^4-n^2\) से (0,12,72,240) मिलते हैं। परीक्षा में उच्च घात वाले विकल्पों को छोटे (n) से जाँचें। / \(n^4-n^2\) gives (0,12,72,240). In exams, test higher-power options with small (n).
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What is the general term of the sequence \(12,27,46,69,\ldots\)?
A. \(a_n=2n^2+9n+1\)
\(2n^2+9n+1\) से (12,27,46,69) मिलते हैं। परीक्षा में वर्गीय नियम को पहले चार पदों से जाँचें। / \(2n^2+9n+1\) gives (12,27,46,69). In exams, test the quadratic rule with the first four terms.
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What is the general term of the sequence \(188,176,164,152,\ldots\)?
B. \(a_n=200-12n\)
(n=1) पर (188) और (n=2) पर (176) मिलता है, इसलिए \(a_n=200-12n\) है। परीक्षा में घटते अनुक्रम के पहले दो पद जाँचें। / At (n=1) it gives (188), and at (n=2) it gives (176), so \(a_n=200-12n\). In exams, check the first two terms of a decreasing sequence.
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Which general term is correct for the sequence \(2,9,21,38,\ldots\)?
A. (a_n=\frac{n(5n-1)}{2})
(\frac{n(5n-1)}{2}) से (2,9,21,38) मिलते हैं। परीक्षा में भिन्न रूप वाले सामान्य पद भी जाँचें। / (\frac{n(5n-1)}{2}) gives (2,9,21,38). In exams, also check fractional-form general terms.
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What is the general term of the sequence \(7,25,61,121,\ldots\)?
A. (a_n=(n+1)3-n)
((n+1)3-n) से (7,25,61,121) मिलते हैं। परीक्षा में स्थानांतरित घन नियमों को जाँचें। / ((n+1)3-n) gives (7,25,61,121). In exams, check shifted cube rules.
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What is the general term of the sequence \(4,21,52,97,\ldots\)?
A. \(a_n=7n^2-4n+1\)
\(7n^2-4n+1\) से (4,21,52,97) मिलते हैं। परीक्षा में दूसरे अंतर समान देखकर वर्गीय नियम पहचानें। / \(7n^2-4n+1\) gives (4,21,52,97). In exams, identify a quadratic rule by equal second differences.
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What is the general term of the sequence \(8,27,56,95,\ldots\)?
D. \(a_n=5n^2+4n-1\)
\(5n^2+4n-1\) से (8,27,56,95) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें। / \(5n^2+4n-1\) gives (8,27,56,95). In exams, test the rule on the first four terms.
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