Insert 6 geometric means between 27 and .
Let the six terms be a1, a2, a3, a4, a5, a6.
And,
A = 27, B
Now, these 6 terms are between A and B.
∴ A, a1, a2, a3, a4, a5, a6, B.
Now all of them are in GP
So we now have 8 terms in GP with the first term being 27 and eighth being 1/81.
We know that, Tn = arn–1
Here Tn = , a = 27 and
⇒
⇒
⇒
∴ a1 = Ar =
a2 = Ar2 =
a3 = Ar3 =
a4 = Ar4 =
a5 = Ar5 =
a6 = Ar6 =
∴ The six GM between 27 and 1/81 are .