Question

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

Answer 1

Sum of first term $=p+q=a$ ……$\left(1\right)$

Sum of first two terms $=2p+4q=a+(a+d)$

$\Rightarrow p+2q=a+\frac{d}{2}$ ……….$\left(2\right)$

Equation $\left(1\right)$ - equation $\left(2\right)$

$-q=-\frac{d}{2}\Rightarrow d=2q$

Common difference.