# If the Sum of N Terms of an Ap is 2n2 + 3n, Then Write Its Nth Term. - Mathematics

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

#### Solution

Given:

$S_n = 2 n^2 + 3n$

$\Rightarrow S_1 = 2 \left( 1 \right)^2 + 3\left( 1 \right)$

$= 5$

$S_2 = 2 \left( 2 \right)^2 + 3\left( 2 \right)$

$= 14$

$\therefore a_1 + a_2 = 14$

$\Rightarrow 5 + a_2 = 14$

$\Rightarrow a_2 = 9$

Common difference, d  = $a_2 - a_1$ = 9  $-$ 5  =  4
nth term = a + $\left( n - 1 \right)d$  = 5+$\left( n - 1 \right)$4
= 4n+1

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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 19 Arithmetic Progression
Q 3 | Page 50