Geometric sequence

Question

 Let x-2, x, x+3 be the first 3 terms of a geometric sequence. Find the value of x..

Please help, been trying to do this for hours and cant come uyp with a good answer, any help would be extremely appreaciated, thanks!

Answer 1

If it's a geometric sequence, then the ratio of successive terms are equal (the common ratio). That is:

(x+3)/x = x/(x-2)

(x+3)(x-2) = x²

x² + x - 6 = x²

Solve for x