Insert 5 geometric means between and .

Question

Philoid · Accepted Answer

Let the five terms be a₁, a₂, a₃, a₄, a₅.

And,

Now these 5 terms are between A and B.

∴ A, a₁, a₂, a₃, a₄, a₅, B.

Now all of them are in GP

So we now have 7 terms in GP with the first term being 32/9 and seventh being 81/2.

∴ T_n = arⁿ^–1

Here T_n = , a = and

⇒

∴ a₁ = Ar =

a₂ = Ar² =

a₃ = Ar³ =

a₄ = Ar⁴ =

a₅ = Ar⁵ =

∴ The six GM between 16 and 1/4 are .