Q. If $S_{n} = nP + \frac{1}{2}n(n - 1)\mathcal{Q}$, where $S_{n}$ denotes the sum of the first $n$ terms of an AP, then the common difference is
A) $P + \mathcal{Q}$
B) $2P + 3\mathcal{Q}$
C) $2\mathcal{Q}$
D) $\mathcal{Q}$
Explanation
(d)
$d = T_{2} - T_{1} = \left( S_{2} - S_{1} \right) - S_{1}$
$= S_{2} - 2S_{1}$
$= 2P + Q - 2P = Q\ \left\lbrack \because S_{n} = \frac{n}{2}\left\{ 2P + (n - 1)\mathcal{Q} \right\} \right\rbrack$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.