Penjelasan dengan langkah-langkah:

Let the three terms of the geometric progression be a, ar, and ar^2, where r > 1. The second term is ar, and if it is doubled, the three terms of the new arithmetic progression are a, 2ar, and ar^2.

Since the three terms form an arithmetic progression, we have:

2ar - a = ar^2 - 2ar

Simplifying this equation, we get:

3ar = ar^2 + a

3r = r^2 + 1

r^2 - 3r + 1 = 0

Solving for r using the quadratic formula, we get:

r = (3 ± sqrt(5))/2

Since r > 1, we take the positive root:

r = (3 + sqrt(5))/2

Therefore, the common ratio of the geometric progression is (3 + sqrt(5))/2.