Is it possible to find the first term of a geometric progression if the number and sum of the first terms are known?

Question

Algebra

How to turn into the desired N, instead of Z? That is, x and z are known in advance.
I am not on friendly terms with algebra (as it is now obvious). Therefore, if the essence of the question is not clear, tell me how to clarify, please.

Answer 1

According to Wikipedia, the sum of the first n terms of a geometric progression:
you get that you know Sn and n. It turns out an equation with two unknowns, which does not have a single solution (you can express one unknown through the other and get a lot of solutions).