2016/113) Let a,b,c be respectively the sum of the first n, next n, and next n terms of a GP. Show that a,b,c are in GP.

Let the first number be p and common ratio be q
so we have $a=p(1+q^2+\cdots+q^{n-1})$ , $b = pq^n(1+q^2+\cdots + q^{n-1})$, $c= pq^2(1+q^2+\cdots+q^{n-1})$
hence$\frac{b}{a} = q^n$ and $\frac{c}{b} = q^n$
or $\frac{b}{a} = \frac{c}{b}$ and as ratios are same so a,b,c are in GP