Question

Find how many terms of G.P. `2/9 - 1/3 + 1/2` ......... must be added to get the sum equal to `55/72`?

Answer 1

Given G.P. : `2/9 - 1/3 + 1/2`

Here,

First term, a = `2/9`

Common ratio, r = `(-1/3)/(2/9) = -3/2 < 1`

Let required number of terms be n.

`=> S_n = 55/72`

`=> (a(1 - r^n))/(1 - r) = 55/72`

`=> (2/9(1 - (-3/2)^n))/(1 - (-3/2)) = 55/72`

`=> (2/9(1 - (-3/2)^n))/(5/2) = 55/72`

`=> 2/9(1 - (-3/2)^n) = 55/72 xx 5/2`

`=> 1 - (-3/2)^n = 55/72 xx 5/2 xx 9/2`

`=> 1 - (-3/2)^n = 275/32`

`=> 1 - 275/32 = (-3/2)^n`

`=> -243/32 = (-3/2)^n`

`=> (-3/2)^5 = (-3/2)^n`

`=>` n = 5

∴ Required number of terms = 5