Question

The sum of 20 terms of the G.P. 10, 20, 40, ..... is ______.

Options

• `10(2^(19) - 1)`

• `10(2^(21) - 1)`

• `10(2^(20) - 1)`

• none of these

Answer 1

The sum of 20 terms of the G.P. 10, 20, 40, ..... is `bbunderline(10(2^(20) - 1))`.

Explanation:

By formula,

Common ratio = `(a_(n+1))/(an)`

Given,

G.P. = 10, 20, 40, ......

a = 10 and r = `20/10`​ = 2.

We know that,

If | r | > 1

Sum of n terms of G.P. (S_n) = `(a(r^n−1))/(r−1)`

Substituting values we get:

⇒ `S_20 = (10(2^20−1))/(2−1)`

= `(10(2^20−1))/1`

= 10(2²⁰ − 1).