Insert two numbers between 3 and 81 so that the resulting sequence is G.P.

Let a₁ and a₂ be two numbers between 3 and 81 such that the series, 3, a₁, a₂, 81, forms a G.P.

Let a₀ be the first term and r be the common ratio of the G.P.

∴81 = ar³

⇒81 = (3)r³

⇒ r³ = 27

∴ r = 3

a₁ = a₀r = (3) (3) = 9

a₂ = a₀ r² = (3) (3)² = 27

∴ The required two numbers are 9 and 27.