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If for each $n \in N, S_{n} = n A + \frac{1}{2} n (n + 1) B$ is sum of the first n terms of an A.P., the common difference of the A.P. is

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A + 2B

A + B

B/2

answer is C.

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Detailed Solution

Use $: a_{n} = S_{n} - S_{n - 1}$ and $d = a_{n} - a_{n - 1} .$

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