The

From the question it is given that,

The n^th term of a G.P.

   

The sum of its n terms

   

Common ratio r =

   

We know that,

   

   

   

… [equation (i)]

Also we know that,

   

   

By cross multiplication we get,

   

   

… [equation (ii)]

Now, consider both the equation(i) and equation (ii)

   

By cross multiplication we get,

   

By simplification,

   

By comparing both LHS and RHS, we get,

Then,

   

Therefore, the value of a is

   

.