Level 47 • 23/50 questions • 25 seconds per question.
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What is the general term of the sequence \(3,10,21,36,\ldots\)?
B. \(a_n=2n^2+n\)
\(2n^2+n\) से (3,10,21,36) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें। / \(2n^2+n\) gives (3,10,21,36). In exams, test the rule on the first four terms.
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What is the general term of the sequence \(2,9,22,41,\ldots\)?
B. \(a_n=3n^2-2n+1\)
\(3n^2-2n+1\) से (2,9,22,41) मिलते हैं। परीक्षा में दूसरे अंतर से वर्गीय नियम पहचानें। / \(3n^2-2n+1\) gives (2,9,22,41). In exams, use second differences to identify a quadratic rule.
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Which general term is correct for the sequence \(4,9,16,25,\ldots\)?
C. (a_n=(n+1)2)
ये \(2^2,3^2,4^2,5^2\) हैं, इसलिए (a_n=(n+1)2) है। परीक्षा में स्थानांतरित वर्ग पहचानें। / These are \(2^2,3^2,4^2,5^2\), so (a_n=(n+1)2). In exams, recognize shifted squares.
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What is the general term of the sequence \(4,15,34,61,\ldots\)?
A. \(a_n=4n^2-n+1\)
\(4n^2-n+1\) से (4,15,34,61) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम जाँचें। / \(4n^2-n+1\) gives (4,15,34,61). In exams, check a quadratic rule when second differences are constant.
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If \(a_n=9n+2\), which term is equal to (146)?
C. (n=16)
(9n+2=146) से (n=16) मिलता है। परीक्षा में पद संख्या के लिए सूत्र को दिए मान के बराबर रखें। / From (9n+2=146), we get (n=16). In exams, equate the formula to the given value to find the term number.
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In the sequence \(6,15,24,33,\ldots\), which term is (150)?
B. सोलहवाँ पद(16)th term
इसका नियम \(a_n=9n-3\) है और (9n-3=150) से (n=17) नहीं, (n=17) मिलता है; इसलिए सही पद सत्रहवाँ है। / Its rule is \(a_n=9n-3\), and (9n-3=150) gives (n=17), so the correct term is the (17)th term.
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What is the general term of the sequence \(2,5,10,17,\ldots\)?
A. \(a_n=n^2+1\)
\(n^2+1\) से (2,5,10,17) मिलते हैं। परीक्षा में वर्ग में स्थिर जोड़ भी जाँचें। / \(n^2+1\) gives (2,5,10,17). In exams, also check constant addition to squares.
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If \(a_n=n^2+1\), which term is equal to (101)?
C. (n=10)
\(n^2+1=101\) से \(n^2=100\) और (n=10) है। परीक्षा में पूर्ण वर्ग पहचानें। / From \(n^2+1=101\), we get \(n^2=100\) and (n=10). In exams, identify perfect squares.
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What is the general term of the sequence \(2,6,22,74,\ldots\)?
A. \(a_n=3^n-2n+1\)
\(3^n-2n+1\) से (2,6,22,74) मिलते हैं। परीक्षा में घात और रैखिक घटाव दोनों जाँचें। / \(3^n-2n+1\) gives (2,6,22,74). In exams, check both the power and linear subtraction.
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Which general term is correct for the sequence \(2,7,17,37,\ldots\)?
A. \(a_n=5\cdot2^{n-1}-3\)
\(5\cdot2^{n-1}-3\) से (2,7,17,37) मिलते हैं। परीक्षा में गुणोत्तर रूप में स्थिर घटाव भी जाँचें। / \(5\cdot2^{n-1}-3\) gives (2,7,17,37). In exams, also check constant subtraction in geometric forms.
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If \(a_n=3n^2+n-2\), what is the sum of the first three terms?
C. (40)
पहले तीन पद (2,12,26) हैं और योग (40) है। परीक्षा में योग से पहले सभी पद लिखें। / The first three terms are (2,12,26), and the sum is (40). In exams, write all terms before adding.
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What is the general term of the sequence \(2,12,26,44,\ldots\)?
A. \(a_n=3n^2+n-2\)
\(3n^2+n-2\) से (2,12,26,44) मिलते हैं। परीक्षा में दूसरे अंतर देखकर वर्गीय नियम चुनें। / \(3n^2+n-2\) gives (2,12,26,44). In exams, choose a quadratic rule by checking second differences.
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What is the general term of the sequence \(2,12,36,80,\ldots\)?
A. \(a_n=n^3+n^2\)
\(n^3+n^2\) से (2,12,36,80) मिलते हैं। परीक्षा में घन और वर्ग वाले संयुक्त नियम जाँचें। / \(n^3+n^2\) gives (2,12,36,80). In exams, check combined cube-and-square rules.
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What is the general term of the sequence \(84,78,72,66,\ldots\)?
B. \(a_n=90-6n\)
(n=1) पर (84) और (n=2) पर (78) मिलता है, इसलिए \(a_n=90-6n\) है। परीक्षा में घटते अनुक्रम के पहले दो पद जाँचें। / At (n=1) it gives (84), and at (n=2) it gives (78), so \(a_n=90-6n\). In exams, check the first two terms of a decreasing sequence.
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Which general term is correct for the sequence \(\frac{5}{2},7,\frac{27}{2},22,\ldots\)?
A. (a_n=\frac{n(2n+3)}{2})
(\frac{n(2n+3)}{2}) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को भी छोटे (n) से जाँचें। / (\frac{n(2n+3)}{2}) gives the given terms. In exams, test fractional terms using small (n).
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What is the general term of the sequence \(3,12,55,240,\ldots\)?
A. \(a_n=4^n-n^2\)
\(4^n-n^2\) से (3,12,55,240) मिलते हैं। परीक्षा में घात में से वर्ग घटाने वाले नियम भी जाँचें। / \(4^n-n^2\) gives (3,12,55,240). In exams, also check rules where a square is subtracted from a power.
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If \(a_n=12n-7\), what is the average of the first five terms?
A. (29)
पहले पाँच पद (5,17,29,41,53) हैं और औसत (29) है। परीक्षा में औसत के लिए योग को पदों की संख्या से भाग दें। / The first five terms are (5,17,29,41,53), and the average is (29). In exams, divide the sum by the number of terms.
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In the sequence \(5,17,29,41,\ldots\), which term is (149)?
B. तेरहवाँ पद(13)th term
इसका नियम \(a_n=12n-7\) है और (12n-7=149) से (n=13) है। परीक्षा में दिए पद को सामान्य पद के बराबर रखें। / Its rule is \(a_n=12n-7\), and (12n-7=149) 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 \(3,21,119,617,\ldots\)?
A. \(a_n=5^n-2n\)
\(5^n-2n\) से (3,21,119,617) मिलते हैं। परीक्षा में घात में से रैखिक पद घटाकर भी जाँचें। / \(5^n-2n\) gives (3,21,119,617). In exams, also check subtraction of a linear term from a power.
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Which general term is correct for the sequence \(5,18,35,56,\ldots\)?
A. \(a_n=2n^2+7n-4\)
\(2n^2+7n-4\) से (5,18,35,56) मिलते हैं। परीक्षा में वर्गीय नियम को छोटे (n) से जाँचें। / \(2n^2+7n-4\) gives (5,18,35,56). In exams, test the quadratic rule with small (n).
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What is the general term of the sequence \(\frac{7}{3},6,11,\frac{52}{3},\ldots\)?
A. \(a_n=\frac{2n^2+5n}{3}\)
\(\frac{2n^2+5n}{3}\) से दिए पद मिलते हैं। परीक्षा में भिन्न पदों को भी विकल्पों से मिलाएँ। / \(\frac{2n^2+5n}{3}\) gives the given terms. In exams, match fractional terms with options too.
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What is the general term of the sequence \(9,24,47,78,\ldots\)?
A. \(a_n=4n^2+3n+2\)
\(4n^2+3n+2\) से (9,24,47,78) मिलते हैं। परीक्षा में दूसरे अंतर समान हों तो वर्गीय नियम जाँचें। / \(4n^2+3n+2\) gives (9,24,47,78). In exams, check a quadratic rule when second differences are constant.
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What is the general term of the sequence \(6,20,42,72,\ldots\)?
D. \(a_n=4n^2+2n\)
\(4n^2+2n\) से (6,20,42,72) मिलते हैं। परीक्षा में पहले चार पदों पर नियम जाँचें। / \(4n^2+2n\) gives (6,20,42,72). In exams, test the rule on the first four terms.
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