Question

Find the common ratio of an infinite geometric series with the given sum and first term

S=9,a1=3

Answer 1

Given S  =  9 and a  =  3.

The sum of the infinite series in GP is

S = a / (1 - r)

Substitute S = 9 and a = 3 in above equation

9  =  3 / (1 - r)

9 (1 - r)  =  3

(1 - r)  =  3/9

1 - r  =  1/3

1 - (1/3)  =  r

(3 - 1)/3  =  r

r  =  2/3

Answer :

The common ratio of GP is r  =  2/3.