Question

Insert two numbers between 1 and – 27 so that the resulting sequence is a G.P.

Answer 1

Let the required numbers be G₁ and G₂.
∴ 1, G₁, G₂, – 27 are in G.P.
∴ t₁ = 1, t₂ = G₁, t₃ = G₂, t₄ = – 27
∴ t₁ = a = 1
t_n = ar^n–1
∴ t₄ = (1)r^4–1
∴ – 27 = r³
∴ r³ = (– 3)³
∴ r = – 3
∴ G₁ = t₂ = ar = 1(– 3) = – 3
G₂ = t₃ = ar² = 1(– 3)² = 9
∴ – 3 and 9 are the required numbers to be inserted between 1 and – 27 so that th resulting sequence is a G.P.