Question

In an A.P., $s_p=q,s_q=pand{s}_r$ denotes the sum of the first r terms. Then $S_{p+q}$ is equal to

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

Answer 1

Answer: (D)

$-(p+q)$

$S_r=$ Sum of first r terms in A.P.

$S_p=q,S_q=p\frac{p}{2}(2a+(p-1\left)d\right)=q\frac{q}{2}(2a+(q-1\left)d\right)=ppa+\frac{p(p-1)}{2}d=qqa+\frac{q(q-1)}{2}d=p(p-q)a+\left(\frac{p^2-p-q^2+q}{2}\right)d=q-p(p-q)a+\frac{(p-q)(p+q-1)}{2}d=q-pa+\frac{(p+q-1)}{2}d=-1(p+q)a+\frac{(p+q)(p+q-1)}{2}d=-(p+q)S_{p+q}=-(p+q)$