Solution:

Consider the first five terms to be a₁, a₂, a₃, a₄, a₅.

we have, A = 27, B = 1/81

The above mentioned five terms are between A and B. So the GP is: A, a₁, a₂, a₃, a₄, a₅, B. Therefore, we can say that there are 7 terms in GP with the first term being 16 and the seventh being 1/4.

We know that,

T_n = ar^n–1

Here, T_n = 1/4, a = 16 and

$ 1/4\text{ }=\text{ }16{{r}^{7-1}} $

$ 1/\left( 4\times 16 \right)\text{ }=\text{ }{{r}^{6}} $

$ r\text{ }=\text{ }1/2 $

$ {{a}_{1}}~=\text{ }Ar\text{ }=\text{ }16\times 1/2\text{ }=\text{ }8 $

$ {{a}_{2}}~=\text{ }A{{r}^{2}}~=\text{ }16\times 1/4\text{ }=\text{ }4 $

$ {{a}_{3}}~=\text{ }A{{r}^{3}}~=\text{ }16\times 1/8\text{ }=\text{ }2 $

$ {{a}_{4}}~=\text{ }A{{r}^{4}}~=\text{ }16\times 1/16\text{ }=\text{ }1 $

$ {{a}_{5}}~=\text{ }A{{r}^{5}}~=\text{ }16\times 1/32\text{ }=\text{ }1/2 $

∴ The five GM between 16 and 1/4 are 8, 4, 2, 1, ½