Question

If the second term in a geometric sequence is 20 and the fourth term is 11.25, what is the common ratio

Answer 1

So between the second and fourth term, you are multiplying by r².
20 * r² = 45/4
r² = 45/80
r² = 9/16
r = √(9/16)
r = ± (3/4)

So there are two possible common ratios:
r = -3/4
or
r = 3/4