Question

A G.P. consists of an even number of terms. The sum of all its terms is five times the sum of odd terms. Then the common ratio of this progression is ...............

Answer 1

Let the terms of the G.P. be $a,ar,a{r}^2,...$
The sum of all terms = $\frac{a(r^n-1)}{(r-1)}$
The odd terms look like $a,a{r}^2,a{r}^4,...$ whose sum will be $\frac{a(r^n-1)}{r^2-1}$
According to the given conditions, $\frac{a(r^n-1)}{(r-1)}=5\times \frac{a(r^n-1)}{r^2-1}$
$\Rightarrow r+1=5$
$\Rightarrow r=4$