quadratic-pattern se related questions ko ek jagah revise karein. Har question me bilingual content, answer feedback aur explanation available hai.
18 questions tagged with quadratic-pattern.
What is the (n)th term of the sequence \(4,16,36,64,\ldots\)?
A. \(4n^2\)
पद (4(1)2,4(2)2,4(3)2,\ldots) हैं, इसलिए \(a_n=4n^2\)। वर्ग और गुणक दोनों पहचानें। / The terms are (4(1)2,4(2)2,4(3)2,\ldots), so \(a_n=4n^2\). Identify both the square and the multiplier.
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What is the (n)th term of the sequence \(7,16,27,40,\ldots\)?
A. \(n^2+6n\)
\(n^2+6n\) रखने पर (7,16,27,40) मिलते हैं। पहले चार पदों पर नियम जांचें। / Putting \(n^2+6n\) gives (7,16,27,40). Check the rule on the first four terms.
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What is the (n)th term of the sequence \(4,10,18,28,\ldots\)?
A. \(n^2+3n\)
\(n^2+3n\) रखने पर (4,10,18,28) मिलते हैं। वर्ग और रैखिक भाग दोनों पहचानें। / Putting \(n^2+3n\) gives (4,10,18,28). Identify both the square and linear parts.
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What is the (n)th term of the sequence \(9,15,23,33,\ldots\)?
A. \(n^2+3n+5\)
\(n^2+3n+5\) रखने पर (9,15,23,33) मिलते हैं। पहले कुछ पदों पर नियम जांचें। / Putting \(n^2+3n+5\) gives (9,15,23,33). Check the rule on the first few terms.
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Which is the correct (n)th term for the sequence \(8,13,20,29,\ldots\)?
A. \(n^2+2n+5\)
\(n^2+2n+5\) रखने पर (8,13,20,29) मिलते हैं। पहले कुछ पदों पर नियम जांचें। / Putting \(n^2+2n+5\) gives (8,13,20,29). Check the rule on the first few terms.
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What is the (n)th term of the sequence \(6,9,14,21,\ldots\)?
A. \(n^2+5\)
पद \(1^2+5,2^2+5,3^2+5,\ldots\) हैं, इसलिए \(a_n=n^2+5\)। वर्ग के साथ स्थिर जोड़ पहचानें। / The terms are \(1^2+5,2^2+5,3^2+5,\ldots\), so \(a_n=n^2+5\). Identify the square plus a constant.
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What is the (n)th term of the sequence \(3,12,27,48,\ldots\)?
A. \(3n^2\)
पद (3(1)2,3(2)2,3(3)2,\ldots) हैं, इसलिए \(a_n=3n^2\)। वर्ग और गुणक दोनों पहचानें। / The terms are (3(1)2,3(2)2,3(3)2,\ldots), so \(a_n=3n^2\). Identify both the square and the multiplier.
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What is the (n)th term of the sequence \(5,12,21,32,\ldots\)?
A. \(n^2+4n\)
\(n^2+4n\) रखने पर (5,12,21,32) मिलते हैं। पहले चार पदों पर नियम जांचें। / Putting \(n^2+4n\) gives (5,12,21,32). Check the rule on the first four terms.
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What is the (n)th term of the sequence \(7,11,17,25,\ldots\)?
A. \(n^2+n+5\)
\(n^2+n+5\) रखने पर (7,11,17,25) मिलते हैं। पहले कुछ पदों पर नियम जांचें। / Putting \(n^2+n+5\) gives (7,11,17,25). Check the rule on the first few terms.
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Which is the correct (n)th term for the sequence \(6,10,16,24,\ldots\)?
A. \(n^2+5\)
पद \(1^2+5,2^2+6\) नहीं; सही जांच में \(n^2+5\) से (6,9,14) नहीं मिलता। सही पैटर्न \(n^2+n+4\) है। / Checking shows \(n^2+5\) does not match all terms. The correct pattern is \(n^2+n+4\).
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What is the (n)th term of the sequence \(3,6,11,18,\ldots\)?
A. \(n^2+2\)
पद \(1^2+2,2^2+2,3^2+2,\ldots\) हैं, इसलिए \(a_n=n^2+2\)। वर्ग के साथ स्थिर जोड़ पहचानें। / The terms are \(1^2+2,2^2+2,3^2+2,\ldots\), so \(a_n=n^2+2\). Identify the square plus a constant.
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What is the (n)th term of the sequence \(2,8,18,32,\ldots\)?
A. \(2n^2\)
पद (2(1)2,2(2)2,2(3)2,\ldots) हैं, इसलिए \(a_n=2n^2\)। वर्ग और गुणक दोनों पहचानें। / The terms are (2(1)2,2(2)2,2(3)2,\ldots), so \(a_n=2n^2\). Identify both the square and the multiplier.
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What is the (n)th term of the sequence \(3,8,15,24,\ldots\)?
B. \(n^2+2\)
पद \(1^2+2,2^2+4\) नहीं; सही पैटर्न \(n^2+2n\) से (3,8,15,24) मिलता है। विकल्प में \(n^2+2n\) चुनें। / The rule \(n^2+2n\) gives (3,8,15,24). Choose the option that matches all first terms.
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What is the (n)th term of the sequence \(4,7,12,19,\ldots\)?
A. \(n^2+3\)
पद \(1^2+3,2^2+3,3^2+3,\ldots\) हैं, इसलिए \(a_n=n^2+3\)। वर्ग के साथ स्थिर जोड़ पहचानें। / The terms are \(1^2+3,2^2+3,3^2+3,\ldots\), so \(a_n=n^2+3\). Identify the square plus a constant.
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Which is the correct (n)th term for the sequence \(5,8,13,20,\ldots\)?
A. \(n^2+4\)
पद \(1^2+4,2^2+4,3^2+4,\ldots\) हैं, इसलिए \(a_n=n^2+4\)। वर्ग के साथ स्थिर संख्या पहचानें। / The terms are \(1^2+4,2^2+4,3^2+4,\ldots\), so \(a_n=n^2+4\). Identify the square with the constant number.
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What is the correct sum of the first (6) terms of the sequence \(3,7,13,21,31,\ldots\)?
D. (118)
छठा पद (43) है और योग (3+7+13+21+31+43=118) है। योग में सभी (6) पद शामिल करें। / The sixth term is (43), and the sum is (3+7+13+21+31+43=118). Exam tip: include all (6) terms in the sum.
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What is the sum of the first (6) terms of the sequence \(3,7,13,21,31,\ldots\)?
B. (114)
छठा पद (43) है और योग (3+7+13+21+31+43=118) नहीं बल्कि (118) है। विकल्पों में (118) सही है। / The sixth term is (43), and the sum is (3+7+13+21+31+43=118). Therefore (118) is correct.
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What will be the (12)th term in the sequence \(3,5,9,15,23,\ldots\)?
B. (135)
यहाँ \(a_n=n^2-n+3\) है इसलिए \(a_{12}=144-12+3=135\) है। शुरुआती अंतरों से सूत्र पहचानें। / Here \(a_n=n^2-n+3\), so \(a_{12}=144-12+3=135\). Exam tip: identify the formula from initial differences.
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