Question -
Answer -
Let the five terms bea1, a2, a3, a4, a5.
A = 32/9, B = 81/2
Now, these 5terms are between A and B.
So the GP is: A, a1,a2, a3, a4, a5, B.
So we now have 7 termsin 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 GMbetween 32/9 and 81/2 are 16/3, 8, 12, 18, 27