Question

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

Answer 1

Let G₁ and G₂ be two numbers between 3 and 81 such that the series, 3,

G₁, G₂, 81, forms a G.P.

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

∴ 81 = (3) (r)³

⇒ r³ = 27

∴ r = 3 (Taking real roots only)

For r = 3,

G₁ = ar = (3) (3) = 9

G₂ = ar² = (3) (3)² = 27

Thus, the required two numbers are 9 and 27.