If the and terms of a G.P. are and respectively, show that its term is

Solution:

The term of Geometric Progression is given by in which the first term is and the common difference is

term is given as

Above equation can also be re-written as

When we rearrange the above equation we obtain

Above equation can also be re-written as

When we rearrange the above equation we obtain

From eq.(a) and eq.(b) we have

When we rearrange we obtain

term is given by

But and the term is

But

By using the laws of exponents we obtain

On rearranging

Now take LCM and simplify it

As a result hence proved.