Question

If the sum of an infinite G.P. be 9 and the sum of first two terms be 5, then the common ratio is.

• A. 1/3
• B. 3/2
• C. ¾
• D. 2/3

Answer 1

Answer: (D)

2/3

Answer 2

Infinite series is

Sum $S = \frac { a } { 1 - r } = 9 \Rightarrow a = 9 ( 1 - r )$ …..(i)

And $a + a r = 5$

$\Rightarrow a ( 1 + r ) = 5 \Rightarrow 9 ( 1 - r ) ( 1 + r ) = 5$ [By equation (i)]

$1 - r ^ { 2 } = \frac { 5 } { 9 } \Rightarrow r = \pm \frac { 2 } { 3 }$.