If the sum of n terms of an AP is 2n² + 3n, then write its nth term.

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Solution

Given:
$S_{n} = 2 n^{2} + 3 n$
$\Rightarrow S_{1} = 2 {(1)}^{2} + 3 (1) = 5 S_{2} = 2 {(2)}^{2} + 3 (2) = 14 ∴ a_{1} + a_{2} = 14 \Rightarrow 5 + a_{2} = 14 \Rightarrow a_{2} = 9$

Common difference, d = $a_{2} - a_{1}$
= 9 $-$ 5
= 4
nth term = a + $(n - 1) d$
= 5+ $(n - 1)$ 4
= 4n+1

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