The sum of the first three terms of a G.P. is 39 / 10, and their product is 1 . Find the common ratio and the terms.

Solution:

Let the three numbers be
According to the question
eq. (1)
eq.
From eq. (2) we obtain,

From eq. (1) we obtain,

eq. (3)
On substituting in 3 we obtain

eq. (4)

The equation will now be,

As a result, the three numbers are