Question

If the sum of n terms of an A.P in $nP+\frac{1}{2}n(n-1)Q$, where P and Q are constants, find the common difference.

Answer 1

$S_n=nP+\frac{1}{2}n(n-1)Q$ [Given]
$S_n=\frac{n}{2}[2n+(n-1\left)Q\right]\dots \dots \left(i\right)$
We know
$S_n=\frac{n}{2}[2a+(n-1\left)d\right]\dots \dots \left(ii\right)$
Where a = first term and d = common difference comparing (i) and (ii)
d = Q
$\therefore$ The common difference is Q.