Second term of a geometric progression is 6 and its fifth term is 9 times of its third term. Find the geometric progression. Consider that each term of the G.P. is positive.

Let first term of the G.P. be a and it's common ratio be r.

Given,

⇒ a₂ = 6

⇒ ar = 6 ……..(i)

Also,

⇒ a₅ = 9a₃

⇒ ar⁴ = 9ar²

⇒ $\dfrac{\text{ar}^4}{\text{ar}^2}$ = 9

⇒ r² = 9

⇒ r = √9

⇒ r = ±3

As all terms of G.P. are positive so, r ≠ -3

∴ r = 3

Substituting r in (i),

⇒ 3a = 6

⇒ a = 2.

G.P. = a, ar, ar², ar³, ……

= 2, 6, 18, 54, …….

Hence, G.P. = 2, 6, 18, 54, …….