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

Question

Philoid · Accepted Answer

Let there be n terms.

a, ar, ar², ar³, ……………..arⁿ ^{- 2}, arⁿ ^{- 1}

The sum of a G.P.

Odd terms of the sequence are:

a, ar², ar⁴……………..ar^{n - 2}

So sum of this series =

⇒

According to the given problem:

⇒

⇒ r + 1 = 5

⇒ r = 4.