Find three numbers in G.P. whose sum is 65 and whose product is 3375.

Solution:

According to the question
equation (1)
equation (2)
From eq.(2) we obtain,

From eq.(1) we obtain,

eq.(3)
By substituting in eq.(3) we obtain


On dividing eq.(4) by 5 we obtain

The eq. will now be
or

So the terms are or
As a result, the three numbers are