Question

If the sum of $p$ terms of an AP with non-zero common difference is equal to the sum of its $q$ terms, then the sum of its $(p+q)$ terms will be

• A. $pq$
• B. $(p-q)$
• C. $0$
• D. $(p+q)$

Answer 1

The correct option is C $0$

$S_p=S_q$
$\Rightarrow \frac{p}{2}[2a+(p-1)d]=\frac{q}{2}[2a+(q-1)d]$
$\Rightarrow 2a(p-q)+d(p^2-p-q^2+q)=0\Rightarrow (p-q)[2a+d(p+q-1)]=0\Rightarrow 2a+(p+q-1)d=0\Rightarrow S_{p+q}=0$