Question

If the sum of $n$ terms of an $A.P$ is $(pn+q{n}^2)$, where $p$ and $q$ are constants, find the common difference?

Answer 1

Let the first term of A.P be a and the common difference be d .

The $\frac{n}{2}$[$2a+(n-1)d$] = ($pn+q{n}^2$)

Equating the coefficients we find $\frac{d}{2}$ = $q$

So, $d=2q$