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

Let `a` is the first term of GP and `r` is the common ratio and there are `2n` terms in GP.

Then, GP will be,

`a,ar,ar^2,ar^3...ar^(2n-1)`

Sum of all `2n` terms of this GP will be,

`S_(2n) = (a(r^(2n)-1))/(r-1)`

All odd terms in this GP will be,

`a,ar^2,ar^4,...ar^(2n-2)`

It is another GP with first term `a` and common ratio `r^2` with `n` terms.

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