Question

The sum of the first $n$ terms of an AP is given by $S_n=2n^2+5n$. Find the common difference of the AP.

Answer 1

$S_n=\frac{n}{2}(2a+(n-1\left)d\right)=an+\frac{n^2}{2}d-\frac{dn}{2}$

Comparing above equation with $S_n=2n^2+5n$

$\frac{d}{2}=2\Rightarrow d=4$