Question

The fifth term of a G.P. is 81 and its second term is 24. Find the geometric progression.

Answer 1

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

5^th term = 81 `=>` ar⁴ = 81

2^nd term = 24 `=>` ar = 24

Now, `(ar^4)/(ar) = 81/24`

`=> r^3 = 27/8`

`=> r = 3/2`

ar = 24

`=> a xx 3/2 = 24`

`=>` a = 16

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

= `16, 24, 16 xx (3/2)^2, 16 xx (3/2)^3,.........`

= 16, 24, 36, 54, ........