The sum of the first k terms of a series S is 3k^{2}+5k. Which one of the following is correct?
- A. The terms of S form an arithmetic progression with common difference 14.
- B. The terms of S form an arithmetic progression with common difference 6. ✓
- C. The terms of S form a geometric progression with common ratio 10/7.
- D. The terms of S form a geometric progression with common ratio 11/4.
Correct Answer: B. The terms of S form an arithmetic progression with common difference 6.
Explanation
The sum S_k = 3k^2 + 5k. The k-th term is T_k = S_k - S_{k-1} = 6k + 2. Since T_k is linear in k, it forms an AP. The common difference is T_k - T_{k-1} = 6.
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