Question -
Answer -
Let the five terms bea1, a2, a3, a4, a5.
A = 27, B = 1/81
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 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 GMbetween 16 and 1/4 are 8, 4, 2, 1, ½