The sum of an infinite geometric series with positive terms is 3 and the sums of the cubes of its terms is `(27)/(19)`. Then the common ratio of this series is

Options

A. `2/9`
B. `4/9`
C. `2/3`
D. `1/3`

Answer

C

Explanation

For first term ‘a’ and common ratio ‘r’
It is given that `a/(1-r)`=3 and `a^3/(1-r^3)=27/19`
`rArr ((1-r^3))/((1-r)^3)=19 rArr (1+r+r^2)/(1-2r+r^2)=19 rArr 6r^2 - 13r+6 =0`
(3r-2)(2r-3)=0
`r=2/3,3/2`
For finite sum of G.P. `r=2/3` is suitable value.