Question -
Answer -
Let the five terms bea1, a2, a3, a4, a5.
A = 32/9, B = 81/2
Now,┬аthese 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,┬аTn┬а=arnтАУ1
Here, Tn┬а=┬а81/2,a = 32/9 and
81/2 = 32/9r7-1
(81├Ч9)/(2├Ч32) = r6
r = 3/2
a1┬а=Ar = (32/9)├Ч3/2 = 16/3
a2┬а=Ar2┬а= (32/9)├Ч9/4 = 8
a3┬а=Ar3┬а= (32/9)├Ч27/8 = 12
a4┬а=Ar4┬а= (32/9)├Ч81/16 = 18
a5┬а=Ar5┬а= (32/9)├Ч243/32 = 27
тИ┤┬аThe five GMbetween 32/9 and 81/2 are 16/3, 8, 12, 18, 27