If $S_{n}$ , the sum of first n terms of an AP, is given by $5 n^{2} + 3 n$ , then find its nth term.

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Solution

$a_{n} = S_{n} - S_{n - 1}$
$a_{n} = (5 n^{2} + 3 n) - [5 (n - 1)^{2} + 3 (n - 1)]$
$a_{n} = (5 n^{2} + 3 n) - (5 n^{2} - 7 n + 2)$
$a_{n} = 10 n - 2$

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If Sn, the sum of first n terms of an AP, is given by 5n2+3n, then find its nth term.

an=Sn−Sn−1an=(5n2+3n)−[5(n−1)2+3(n−1)]an=(5n2+3n)−(5n2−7n+2)an=10n−2

If $S_{n}$ , the sum of first n terms of an AP, is given by $5 n^{2} + 3 n$ , then find its nth term.

$a_{n} = S_{n} - S_{n - 1}$
$a_{n} = (5 n^{2} + 3 n) - [5 (n - 1)^{2} + 3 (n - 1)]$
$a_{n} = (5 n^{2} + 3 n) - (5 n^{2} - 7 n + 2)$
$a_{n} = 10 n - 2$