If the sum of an infinite GP be 9 and sum of first two terms be 5 them their common ratio is . . .

Options

A. `(1)/(3)`
B. `3`
C. `(2)/(3)`
D. `(3)/(2)`

Answer

C

Explanation

We have,
sum of infinite `GP,(a)/(1-r)=9 impliesa=9(1-r)`
and sum of first two terms of a GP in 5
`impliesa+ar=5impliesa(1+r)=5`
`implies9(1-r)(1+r)=5`
`implies1-r^(2)=(5)/(9)impliesr^(2)=(4)/(9)impliesr=(2)/(3)`