Question

In a Geometric Progression (G.P.), the first term is 24 and the fifth term is 8. Find the ninth term of the G.P.

Answer 1

Given: a = 24, t_n = 8

To find: t₉ = ?

Formula: t_n = arⁿ⁻¹

8 = ar⁵⁻¹ 

8 = ar⁴

8 = 24r⁴ 

`r^4 = 8/24`

`r^4 = 1/3`

`(r^4)^2 = (1/3)^2`   ...(Taking the square root on both sides.)

`r^8 = 1/9`

By formula,

Ninth term of G.P. (a₉) = ar⁸

= `24 xx 1/9`

= `8/3`

∴ The ninth term of the G.P. is `8/27`.