Find the sum of n terms of the A.P. whose kth term is 5k + 1.

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Solution

Here,
$a_{k} = 5 k + 1 a_{1} = 5 + 1 = 6 a_{2} = 5 (2) + 1 = 11 a_{3} = 5 (3) + 1 = 16 d = 11 - 6 = 16 - 11 = 5 S_{n} = \frac{n}{2} [2 a + (n - 1) d] = \frac{n}{2} [2 (6) + (n - 1) (5)] = \frac{n}{2} [12 + 5 n - 5] S_{n} = \frac{n}{2} (5 n + 7)$

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