I have a question regarding a solution

The 1st, 4th, and 8th terms of an AP are themselves geometric progression. What is the common ratio of the GP?

where:

1st term = a

4th term = a+3d

8th term = a+7d

The solution given by my teacher is apparently:

(a+3d) ^2 = a (a+7d)

9d^2 = ad

d ( 9d-a) = 0

a = 9d

So numbers in AP are

9d, 12d , 16d

r = 12/9 = 4/3

what formula was **(a+3d) ^2 = a (a+7d) **from?

Gravy May 14, 2023