Question

The first term of a G.P. is 27 and its 8^th term is `1/81`. Find the sum of its first 10 terms.

The first term of a G.P. in 27. If the 8^th term be `1/81`, what will be the sum of 10 terms?

Answer 1

Given,

First term, a = 27

8^th term = ar⁷ = `1/81`

n = 10

Now,

`(ar^7)/a = (1/81)/27`

`=> r^7 = 1/2187`

`=> r^7 = (1/3)^7`

`=> r = 1/3`  ...(∵ r < 1)

∴ `S_n = (a(1 - r^n))/(1 - r)`

`=> S_10 = (27(1 - (1/3)^10))/(1 - 1/3)`

= `(27(1 - 1/3^10))/(2/3)`

= `(27 xx 3)/2(1 - 1/3^10)`

= `81/2 (1 - 1/3^10)`