The sum of the first k terms of a series S is 3k² + 5k. Which one of the following is correct?
Answer
The correct answer is B: The terms of S form an arithmetic progression with common difference 6.. Given S_k = 3k² + 5k. The k-th term is a_k = S_k - S_{k-1} = (3k² + 5k) - (3(k-1)² + 5(k-1)) = 3k² + 5k - 3k² + 6k - 3 - 5k + 5 =…
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.✓ Correct
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.
Explanation
Given S_k = 3k² + 5k. The k-th term is a_k = S_k - S_{k-1} = (3k² + 5k) - (3(k-1)² + 5(k-1)) = 3k² + 5k - 3k² + 6k - 3 - 5k + 5 = 6k + 2. So a_1 = 8, a_2 = 14, a_3 = 20. The common difference is 14 - 8 = 6, confirming an arithmetic progression with common difference 6.
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