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NDA 2025 Maths · Mathematics · Sequences and Series · medium

The sum of the first n terms of an AP is 3n^2+2n. The common difference is

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The sum of the first nn terms of an AP is 3n2+2n3n^2+2n. The common difference is
  1. A. 66
  2. B. 55
  3. C. 33
  4. D. 1111
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Answer: (A) 66

a1=S1=5a_1=S_1=5 and S2=16S_2=16, so a2=11a_2=11. Hence d=a2−a1=6d=a_2-a_1=6. In general Sn−Sn−1=6n−1S_n-S_{n-1}=6n-1, whose difference between consecutive terms is 66; the coefficient 33 of n2n^2 is half of dd.
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