Hi,if we are given two equidistant terms of a geometric progression and also the sum of its terms , then how can we find the actual terms of the G.P? e.g if we are given the 3rd and last terms of the G.P as 12 and 48 and the sum of terms is 393 then the number of terms is 7 and they are: 3,6,12,24,48,96,192 .

I am aware of the following relations:

1. The sum of terms of G.P = a(r^n-1)/(r-1)

2. Product of equidistant terms of a G.P = product of extremes.

But am not sure how to apply them here to get the result.

Thanks.