Question

The product of 3^rd and 8^th terms of a G.P. is 243. If its 4^th term is 3, find its 7^th term.

Answer 1

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

Now,

t₃ × t₈ = 243

`=>` ar² × ar⁷ = 243

`=>` a²r⁹ = 243  ...(i)

Also,

t₄ = 3

`=>` ar³ = 3

`=> a =3/r^3`

Substituting the value of a in (i), we get

`(3/r^3)^2 xx r^9 = 243`

`=> 9/r^6 xx r^9 = 243`

`=>` r³ = 27
`=>` r = 3

`=> a = 3/3^3`

= `3/27`

= `1/9`

∴ 7^th term = t₇

= ar⁶

= `1/9 xx (3)^6`

= 81