Question

If $S_n=nP+\frac{n}{2}(n-1)Q,$ where $S_n$ denotes the sum of the first $n$ terms of an A.P., then the common difference is

• A. $P+Q$
• B. $2P+3Q$
• C. $2Q$
• D. $Q$

Answer 1

The correct option is D $Q$

$S_n=\frac{n}{2}(2a+(n-1\left)d\right)$
where $a:$ first term of the AP, $d:$ common difference
We get,
$\frac{n}{2}(2a+(n-1\left)d\right)=nP+\frac{n}{2}(n-1)Q$
On comparing the coefficients of the respective powers of $n,d=Q$