A G.P. consists of an even number of terms. If the sum of all the terms is 5 times the sum of terms occupying odd places, then find its common ratio.

Explanation

To solve the problem, we need to find the common ratio \( r \) of a geometric progression (G.P.) with an even number of terms, given that the sum of all terms is 5 times the sum of the terms occupying odd places.

### Step-by-Step Solution:

1. **Define the Terms of the G.P.:**
Let the total number of terms in the G.P. be \( 2n \) (since it is given to be even). Let the first term be \( a \) and the common ratio be \( r \). The terms of the G.P. will be:
\[
a, ar, ar^2, ar^3, \ldots, ar^{2n-1}
...