Question

If the 4^th and 9^th terms of a G.P. are 54 and 13122 respectively, find the G.P. Also, find its general term.

Answer 1

Let the first term of the G.P. be a and its common ratio be r.

4^th term = t₄ = 54 `=>` ar³ = 54

9^th term = t₉ = 13122 `=>` ar⁸ = 13122

`(ar^8)/(ar^3) = 13122/54`

`=>` r⁵ = 243

`=>` r = 3

ar³ = 54

`=>` a × (3)³ = 54

`=> a = 54/27 = 2`

∴ Required G.P. = a, ar, ar², ar³, ........

= 2, 2 × 3, 2 × (3)², 54

= 2, 6, 18, 54

General term = t_n

= ar^{n – 1}

= 2 × (3)^{n – 1}