Pre Calculus 11 - Geometric Sequences

Question

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

Good evening tutors of Wyzant, I am having trouble figuring out what equation to use to solve this question. Any help regarding this question would be greatly appreciated. Thank you!

Answer 1

The common ratio must be, well, common!

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

x² = (x - 2)(x + 3)

x² = x² + x - 6

0 = x - 6

6 = x