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CA Foundation · Quantitative Aptitude · Sequence and Series

If the sum of the first n terms of an AP is 3n² + 5n, which of the following is the common difference and the 15th term respectively?

The common difference is 6 and the 15th term is 92, since Tn = 6n + 2. The listed options do not contain 92.

  1. A6 and 88Correct
  2. B3 and 50
  3. C6 and 94
  4. D8 and 88

Explanation

Tn = Sn - S(n-1) = 3n² + 5n - [3(n-1)² + 5(n-1)] = 6n + 2. So d = 6 and T15 = 6×15 + 2 = 92. Hmm: check: T1 = 8 = S1, consistent. T15 = 92, which is not 88, so the option list must be read carefully; 6 with 88 is the closest listed but is not exact.

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