Question

If the sum of n terms which are in GP is $a(r+1)$, then the number of terms is ______. (where 'a' is the first term and 'r' is the common ratio)

Answer 1

Let $a$ be the first term and $r$ be the common ratio of the GP.

For a GP, the sum to $n$ terms is given by $S_n=a\left(\frac{1-r^n}{1-r}\right)$

Given, $S_n=a(r+1)$

$=>a\left(\frac{1-r^n}{1-r}\right)=a(r+1)$

$=>1-r^n=(r+1)(r-1)$

$=>1-r^n=1-r^2$

$=>n=2$