Question

If the sum of first 6 terms is 9 times to the sum of first 3 terms of the same G.P., then common ratio of the series will be

Answer 1

Let a be the first term and r be the common ratio of the GP.

Sum of n terms of GP, Sn = a(r^(n)-1)/(r-1)

Given S6= 9S3

a(r⁶-1)/(r-1) = 9 a(r³-1)/(r-1)

(r⁶-1) = 9 (r³-1)

(r³-1)(r³+1) = 9(r³-1)

(r³+1) = 9

r³ = 8

r = 2

 

 

The common ratio of the series is r=2.