# If the sum of n terms of an AP is given by

Question:

If the sum of $n$ terms of an $A P$ is given by $S_{n}=\left(2 n^{2}+3 n\right)$, then find its common difference.

Solution:

Given: $S_{n}=\left(2 n^{2}+3 n\right)$

To find: find common difference

To find: find common difference

Put $n=1$ we get

$S_{1}=5$ OR we can write

$a=5 \ldots$ equation 1

Similarly put $\mathrm{n}=2$ we get

$\mathrm{S}_{2}=14 \mathrm{OR}$ we can write

$2 a+d=14$

Using equation 1 we get

d = 4