Question -
Answer -
Let the six terms be a1,a2, a3, a4, a5, a6.
A = 27, B = 1/81
Now,┬аthese 6terms are between A and B.
So the GP is: A, a1,a2, a3, a4, a5, a6, B.
So we now have 8 termsin GP with the first term being 27 and eighth being 1/81.
We know that,┬аTn┬а=arnтАУ1
Here, Tn┬а=┬а1/81,a = 27 and
1/81 = 27r8-1
1/(81├Ч27) = r7
r = 1/3
a1┬а=Ar = 27├Ч1/3 = 9
a2┬а=Ar2┬а= 27├Ч1/9 = 3
a3┬а=Ar3┬а= 27├Ч1/27 = 1
a4┬а=Ar4┬а= 27├Ч1/81 = 1/3
a5┬а=Ar5┬а= 27├Ч1/243 = 1/9
a6┬а=Ar6┬а= 27├Ч1/729 = 1/27
тИ┤┬аThe six GMbetween 27 and 1/81 are 9, 3, 1, 1/3, 1/9, 1/27