​ Insert 5 geometric means between 32/9 and 81/2.

Question

Insert 5 geometric means between \(\frac{32}{9}\) and \(\frac{81}{2}\)

Answer 1

Let the five terms be a₁, a₂, a₃, a₄, a₅. 

And,

A = \(\frac{32}{9}\), B = \(\frac{81}{2}\)

Now these 5 terms are between A and B. 

∴ A, a₁, a₂, a₃, a₄, a₅, B. 

Now all of them are in GP 

So we now have 7 terms in GP with the first term being 32/9 and seventh being 81/2.

∴ The six GM between 16 and 1/4 are \(\frac{16}{3}\),8,12,18,27.