Let the five terms be a1, a2, a3, a4, a5.
A = 27, B = 1/81
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 1/4.
We know that, Tn = arn–1
Here, Tn = 1/4, a = 16 and
1/4 = 16r7-1
1/(4 × 16) = r6
r = 1/2
a1 = Ar = 16 × 1/2 = 8
a2 = Ar2 = 16 × 1/4 = 4
a3 = Ar3 = 16 × 1/8 = 2
a4 = Ar4 = 16 × 1/16 = 1
a5 = Ar5 = 16 × 1/32 = 1/2
∴ The five GM between 16 and 1/4 are 8, 4, 2, 1, 1/2