Question

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.

Answer 1

Let there be n terms. 

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

The sum of a G.P. = \(\frac{a(r^n-1)}{r-1}\)

Odd terms of the sequence are:

a, ar², ar⁴……………..ar^{n - 2}

⇒ r + 1 = 5 

⇒ r = 4.