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NDA 2016 Maths · Mathematics · Sequences and Series · medium

The sum of the first n terms of a sequence is Sn=3n^2+2n.

Single correct option

The sum of the first nn terms of a sequence is Sn=3n2+2nS_n=3n^2+2n. Its 10th term is
  1. A. 320320
  2. B. 5959
  3. C. 6565
  4. D. 5656
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Answer: (B) 5959

The nnth term is an=Sn−Sn−1a_n=S_n-S_{n-1}. So a10=S10−S9=(300+20)−(243+18)=320−261=59a_{10}=S_{10}-S_9=(300+20)-(243+18)=320-261=59. The general term is 6n−16n-1, which also gives 5959 at n=10n=10. The number 320 is S10S_{10}, the sum of ten terms rather than the tenth term.
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Original question written in the NDA 2016 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake