Question

In a G.P. the 9^th term is 32805 and 6^th term is 1215. Find the 12^th term

Answer 1

Given, 9^th term = 32805

a.r^n–1 = `1/2817`

t₉ = 32805 [t_n = ar^n–1]

a.r⁸ = 32805 …(1)

6^th term = 1215

a.r⁵ = 1215 …(2)

Divide (1) by (2)

`("ar"^8)/("ar"^5) = 32805/1215`

⇒ r³ = `6561/243`

= `2187/81`

= `729/27`

= `243/9`

= `81/3`

r³ = 27

⇒ r³ = 3³ 

r = 3

Substitute the value of r = 3 in (2)

a.3⁵ = 1215

a × 243 = 1215

a = `1215/243` = 5

Here a = 5, r = 3, n = 12

t₁₂ = `5 xx 3^((12 - 1))`

= 5 × 3¹¹

∴ 12^th term of a G.P. = 5 × 3¹¹