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

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