Question

Insert 4 geometric means between 4 and 972.

Answer 1

Let t₁ = 4, t₂, t₃, t₄, t₅, t₆ = 972 be the sequence. Then;

t₆ = 972 ⇒ ar⁵ = 972 ⇒ 4r⁵ = 972

⇒ r⁵ = 243 = 3⁵ 

⇒ r = 3

Hence the arithmetic means between 4 and 972 are 12, 36, 108, 324.