The sum of n terms of an A.P. is 2n+3 $n^{2}$ . Determine the AP and find its nth term.

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Solution

$S_{n} = 3 n^{2} + 2 n n = 1, S_{1} = 3 \times 2 = 5 n = 2, S_{2} = 3 \times 4 + 2 \times 2 = 16 S u m o f 1^{s t} t e m & 2^{n d} t e r m = 16 S + 2^{n d} t e r m = 16 2^{n d} t e r m = 16 - 5 = 11 N o w, d = 11 - 5 = 6 H e n c e, A P = 5, 11, 17, 23........$

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