Question

Fourth and seventh terms of a G.P. are `1/18` and `-1/486` respectively. Find the G.P.

Answer 1

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

4^th term =`1/18 => ar^3 = 1/18`

7^th term =`1/486 => ar^6 = 1/486`

Now, `(ar^6)/(ar^3) = ((-1)/486)/(1/18)`

`=> r^3 = -1/27`

`=> r = -1/3`

`ar^3 = 1/18`

`=> a xx (-1/3)^3 = 1/18`

`=> a =- 27/18 = -3/2`

∴ G.P. = a, ar, ar², ar³, .......

= `-3/2, -3/2 xx (-1/3), -3/2 xx (-1/3)^2, 1/18, .......`

= `-3/2, 1/2, -1/6,1/18, .......`