Let the five terms be a1, a2, a3, a4, a5.
A = 32/9, B = 81/2
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 32/9 and seventh being 81/2.
We know that, Tn = arn–1
Here, Tn = 81/2, a = 32/9 and
81/2 = 32/9r7-1
(81 × 9)/(2 × 32) = r6
r = 3/2
a1 = Ar = (32/9) × 3/2 = 16/3
a2 = Ar2 = (32/9) × 9/4 = 8
a3 = Ar3 = (32/9) × 27/8 = 12
a4 = Ar4 = (32/9) × 81/16 = 18
a5 = Ar5 = (32/9) × 243/32 = 27
∴ The five GM between 32/9 and 81/2 are 16/3, 8, 12, 18, 27