Question

In an A.P of which 1 is the first term if the sum of the first p terms is zero, then the sum of the (p+q) terms is

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

Let d be the common difference $\Rightarrow S_p=0\Rightarrow \frac{p}{2}[2+(p-1\left)d\right]=0\Rightarrow \frac{2}{1-p}$
The sum of the (p+ q)terms = $S_{p+q}=\frac{(p+q)}{2}[2+(p+q-1\left)d\right]$
$=\frac{(p+q)}{2}[2+(p+q-1\left)\frac{2}{1-p}\right]=\frac{(p+q)}{1-p}[1-p+p+q-1]=\frac{q(p+q)}{1-p}$