If the surn of an infinite GP be 9 and sum of first two terms be 5 then 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`
`implies a = 9 (1 - r)`
and sum of first two terms of a GP in 5
`implies a + ar = 5`
`implies a (1 + r) = 5`
`implies 9 (1 - r) (1 + r) = 5`
`implies 1 - r^(2) = (5)/(9) implies r^(2) = (4)/(9) implies r = (2)/(3)`