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

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Solution

Given $S_{n} = 5 n^{2} + 3 n$

$S_{n - 1} = 5 (n - 1)^{2} + 3 (n - 1)$

$= 5 (n^{2} - 2 n + 1) + 3 n - 3$

$= 5 n^{2} - 10 n + 3 n + 5 - 3$

$= 5 n^{2} - 7 n + 2$

$T_{n} = S_{n} - S_{n - 1}$

$= 5 n^{2} + 3 n - 5 n^{2} + 7 n - 2$

$= 10 n - 2$

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

Given Sn=5n2+3nSn−1=5(n−1)2+3(n−1)=5(n2−2n+1)+3n−3=5n2−10n+3n+5−3=5n2−7n+2Tn=Sn−Sn−1=5n2+3n−5n2+7n−2=10n−2

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

Given $S_{n} = 5 n^{2} + 3 n$

$S_{n - 1} = 5 (n - 1)^{2} + 3 (n - 1)$

$= 5 (n^{2} - 2 n + 1) + 3 n - 3$

$= 5 n^{2} - 10 n + 3 n + 5 - 3$

$= 5 n^{2} - 7 n + 2$

$T_{n} = S_{n} - S_{n - 1}$

$= 5 n^{2} + 3 n - 5 n^{2} + 7 n - 2$

$= 10 n - 2$