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

a = 24 and T₅ = 8, t₉ = ?

t_n = ar^n-1

8 = ar^5-1 

8 = ar⁴

8 = 24r⁴ 

r⁴ = `8/24`

r⁴ = `1/3`

Taking the fourth root on both sides:

r = `(1/3)^(1/4) = 1/sqrt3`

∴ t₉ = ?

t₉ = ar^9-1

t₉ = ar⁸

t₉ = `24 xx (1/sqrt3)^8`

t₉ = `24 xx 1/(sqrt3)^8`

t₉ = `24 xx 1/81`

t₉ = `24/81`

t₉ = `8/27`

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