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

Let first term of the G.P. be a and it's common ratio be r. Given, ⇒ a 5 = 81 ⇒ ar 4 = 81 ........(i) Also, ⇒ a 2 = 24 ⇒ ar = 24 ........(ii) Dividing (i) by (ii) we get, Substituting value of r in (ii) we get, ⇒ a 3 = ar 2 = = = 4 × 9 = 36. ⇒ a 4 = ar 3 = = = 2 × 27 = 54. G.P. = 16, 24, 36, 54, 81, ........... Hence, G.P. = 16, 24, 36, 54, 81, ...........