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CA Foundation · Quantitative Aptitude · Sequence and Series

If Sn = n(n + 3) is the sum of the first n terms of a series, which of the following is true?

The series is an AP with first term 4 and common difference 2. Since Tn = Sn − S(n−1) = 2n + 2, the terms are 4, 6, 8, and so on, with a constant difference of 2 and unequal ratios.

  1. AThe series is an AP with first term 4 and common difference 2Correct
  2. BThe series is a GP with first term 4 and ratio 2
  3. CThe series is an AP with first term 4 and common difference 3
  4. DThe series is neither an AP nor a GP

Explanation

T1 = S1 = 1×4 = 4. For n ≥ 2, Tn = Sn − S(n−1) = n² + 3n − (n−1)² − 3(n−1) = 2n + 2. At n = 1 this gives 4, so the formula holds for all n. Terms 4, 6, 8, ... have constant difference 2, so it is an AP; the ratios 6/4 and 8/6 differ, so it is not a GP.

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