Level 52 • 23/50 questions • 40 seconds per question.
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What is the general term of the sequence \(13,26,39,52,\ldots\)?
A. \(a_n=13n\)
हर पद (13) का गुणज है, इसलिए \(a_n=13n\) है। परीक्षा में गुणज वाले अनुक्रम को (kn) से जाँचें। / Each term is a multiple of (13), so \(a_n=13n\). In exams, check multiple-based sequences using (kn).
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What is the general term of the sequence \(14,20,26,32,\ldots\)?
A. \(a_n=6n+8\)
अंतर (6) है और पहला पद (14) है, इसलिए \(a_n=6n+8\) है। परीक्षा में अंतर को (n) का गुणांक मानें। / The difference is (6) and the first term is (14), so \(a_n=6n+8\). In exams, take the difference as the coefficient of (n).
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Which general term is correct for the sequence \(5,8,13,20,\ldots\)?
B. \(a_n=n^2+4\)
\(n^2+4\) रखने पर (5,8,13,20) मिलते हैं। परीक्षा में विकल्पों को (n=1,2,3) से मिलाएँ। / Using \(n^2+4\) gives (5,8,13,20). In exams, match options using (n=1,2,3).
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What is the general term of the sequence \(28,26,24,22,\ldots\)?
B. \(a_n=30-2n\)
(n=1) पर (28) और (n=2) पर (26) मिलता है, इसलिए \(a_n=30-2n\) है। परीक्षा में घटते अंतर को ऋणात्मक मानें। / At (n=1) it gives (28), and at (n=2) it gives (26), so \(a_n=30-2n\). In exams, treat a decreasing difference as negative.
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What is the general term of the sequence \(7,22,47,82,\ldots\)?
A. \(a_n=5n^2+2\)
\(5n^2+2\) से (7,22,47,82) मिलते हैं। परीक्षा में वर्ग आधारित नियमों को छोटे (n) मानों से जाँचें। / \(5n^2+2\) gives (7,22,47,82). In exams, test square-based rules with small (n) values.
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What is the general term of the sequence \(\frac{5}{2},5,\frac{15}{2},10,\ldots\)?
A. \(a_n=\frac{5n}{2}\)
हर पद \(\frac{5}{2}\) का अगला गुणज है। परीक्षा में भिन्न गुणजों को (kn) के रूप में लिखें। / Each term is the next multiple of \(\frac{5}{2}\). In exams, write fractional multiples as (kn).
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If \(a_n=4n-7\), which term will be equal to (25)?
C. (n=8)
(4n-7=25) से (n=8) मिलता है। परीक्षा में पद संख्या पूछी जाए तो सूत्र को दिए मान के बराबर रखें। / From (4n-7=25), we get (n=8). In exams, when the term number is asked, equate the formula to the given value.
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In the sequence \(-3,1,5,9,\ldots\), which term is (25)?
C. आठवाँ पद(8)th term
इसका नियम \(a_n=4n-7\) है और (4n-7=25) से (n=8) है। परीक्षा में पहले सामान्य पद बनाकर पद संख्या निकालें। / Its rule is \(a_n=4n-7\), and (4n-7=25) gives (n=8). In exams, form the general term first to find the term number.
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Which general term is correct for the sequence \(0,7,26,63,\ldots\)?
B. \(a_n=n^3-1\)
\(n^3-1\) से (0,7,26,63) मिलते हैं। परीक्षा में घन वाले विकल्पों को पहले चार पदों से मिलाएँ। / \(n^3-1\) gives (0,7,26,63). In exams, match cube-based options with the first four terms.
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What is the general term of the sequence \(2,16,54,128,\ldots\)?
A. \(a_n=2n^3\)
ये पद \(2n^3\) से मिलते हैं। परीक्षा में (n=1,2,3) रखकर नियम जाँचें। / These terms come from \(2n^3\). In exams, check the rule by putting (n=1,2,3).
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What is the general term of the sequence \(37,34,31,28,\ldots\)?
B. \(a_n=40-3n\)
(n=1) पर (37) और (n=2) पर (34) मिलता है, इसलिए \(a_n=40-3n\) है। परीक्षा में घटते नियम को पहले पद से जाँचें। / At (n=1) it gives (37), and at (n=2) it gives (34), so \(a_n=40-3n\). In exams, check a decreasing rule with the first term.
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Which general term is correct for the sequence \(11,20,29,38,\ldots\)?
B. \(a_n=9n+2\)
पहला पद (11) और अंतर (9) है, इसलिए \(a_n=9n+2\) है। परीक्षा में पहले दो पदों पर नियम जाँचें। / The first term is (11) and the difference is (9), so \(a_n=9n+2\). In exams, check the rule on the first two terms.
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Which general term is correct for the sequence \(2,5,9,14,\ldots\)?
B. (a_n=\frac{n(n+3)}{2})
(\frac{n(n+3)}{2}) से (2,5,9,14) मिलते हैं। परीक्षा में भिन्न सूत्रों को छोटे (n) मानों से जाँचें। / (\frac{n(n+3)}{2}) gives (2,5,9,14). In exams, test fractional formulas with small (n) values.
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What is the general term of the sequence \(4,22,52,94,\ldots\)?
A. \(a_n=6n^2-2\)
\(6n^2-2\) रखने पर (4,22,52,94) मिलते हैं। परीक्षा में वर्ग वाले नियम को पहले तीन पदों से मिलाएँ। / Using \(6n^2-2\) gives (4,22,52,94). In exams, match the square rule with the first three terms.
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What is the general term of the sequence \(9,27,81,243,\ldots\)?
C. \(a_n=3^{n+1}\)
\(3^{n+1}\) से (9,27,81,243) मिलते हैं। परीक्षा में पहले पद देखकर घातांक का बदलाव पहचानें। / \(3^{n+1}\) gives (9,27,81,243). In exams, use the first term to identify the exponent shift.
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Which general term is correct for the sequence \(4,10,18,28,\ldots\)?
A. \(a_n=n^2+3n\)
\(n^2+3n\) रखने पर (4,10,18,28) मिलते हैं। परीक्षा में बहुपद नियम को पहले चार पदों से जाँचें। / Using \(n^2+3n\) gives (4,10,18,28). In exams, test the polynomial rule with the first four terms.
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What is the general term of the sequence \(54,48,42,36,\ldots\)?
B. \(a_n=60-6n\)
(n=1) पर (54) और (n=2) पर (48) मिलता है, इसलिए \(a_n=60-6n\) है। परीक्षा में घटते अनुक्रम में (n=1) से नियम जाँचें। / At (n=1) it gives (54), and at (n=2) it gives (48), so \(a_n=60-6n\). In exams, check a decreasing sequence rule using (n=1).
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If \(a_n=7n-8\), which term will be equal to (41)?
C. (n=7)
(7n-8=41) से (n=7) मिलता है। परीक्षा में दिए मान को सूत्र के बराबर रखकर हल करें। / From (7n-8=41), we get (n=7). In exams, equate the given value to the formula and solve.
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In the sequence \(-1,6,13,20,\ldots\), which term is (41)?
C. सातवाँ पद(7)th term
इसका नियम \(a_n=7n-8\) है और (7n-8=41) से (n=7) है। परीक्षा में सामान्य पद से पद संख्या निकालें। / Its rule is \(a_n=7n-8\), and (7n-8=41) gives (n=7). In exams, find the term number from the general term.
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What is the general term of the sequence \(1,\frac{5}{3},\frac{7}{3},3,\ldots\)?
B. \(a_n=\frac{2n+1}{3}\)
\(\frac{2n+1}{3}\) से \(1,\frac{5}{3},\frac{7}{3},3\) मिलते हैं। परीक्षा में भिन्न नियमों को छोटे (n) मानों से मिलाएँ। / \(\frac{2n+1}{3}\) gives \(1,\frac{5}{3},\frac{7}{3},3\). In exams, match fractional rules with small (n) values.
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Which general term is correct for the sequence \(15,26,37,48,\ldots\)?
B. \(a_n=11n+4\)
पहला पद (15) और अंतर (11) है, इसलिए \(a_n=11n+4\) है। परीक्षा में अंतर को गुणांक और पहले पद से स्थिर भाग निकालें। / The first term is (15) and the difference is (11), so \(a_n=11n+4\). In exams, use the difference as coefficient and find the constant from the first term.
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What is the general term of the sequence \(5,16,33,56,\ldots\)?
A. \(a_n=3n^2+2n\)
\(3n^2+2n\) से (5,16,33,56) मिलते हैं। परीक्षा में (n=1,2,3) रखकर मिलान करें। / \(3n^2+2n\) gives (5,16,33,56). In exams, substitute (n=1,2,3) and match.
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What is the general term of the sequence \(-2,-2,0,4,\ldots\)?
A. \(a_n=n^2-3n\)
\(n^2-3n\) से (-2,-2,0,4) मिलते हैं। परीक्षा में शून्य या ऋणात्मक पद देखकर नियम को न छोड़ें। / \(n^2-3n\) gives (-2,-2,0,4). In exams, do not reject a rule just because terms are zero or negative.
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