If the sum of n terms of an A.P. is $2 n^{2} + 5 n$ , then its nth term is

4n - 3

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3n - 4

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4n + 3

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3n + 4

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Solution

The correct option is C
4n + 3

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

$S_{1} = {2.1}^{2} + 5.1 = 7$

$∴ a_{1} = 7$

$S_{n} = {2.2}^{2} + 5.2 = 18$

$∴ a_{1} + a_{2} = 18$

$\Rightarrow a_{2} = 11$

Common difference, d = 11 - 7 = 4

$a_{n} = a + (n - 1) d$

= 7 + (n-1)4

= 4n + 3

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