Insert 5 geometric means between 16 and 1/4.

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

A = 27, B = \( \dfrac{1}{4}\)

Now, these 5 terms are between A and B.

So the GP is: A, a₁, a₂, a₃, a₄, a₅, B.

So we now have 7 terms in GP with the first term being 16 and seventh being \(\dfrac{1}{4}\).

We know that, T_n = ar^n–1

Here, T_n = \( \dfrac{1}{4}\), a = 16 and

\( \dfrac{1}{4}\) = 16r^7-1

\( \dfrac{1}{(4×16)}\) = r⁶

r = \( \dfrac{1}{2}\)

a₁ = Ar == 8

a₂ = Ar² = 4

a₃ = Ar³  = 2

a₄ = Ar⁴ = 1

a₅ = Ar⁵ = \( \dfrac{1}{2}\)

The five GM between 16 and \( \dfrac{1}{4}\) are 8, 4, 2, 1, \( \dfrac{1}{2}\)