Question

the 2nd term in a geometric sequence is 20 the 4th term in the same sequence is 45/4 or 11.25 what is the common ratio?

Answer 1

Let x be the common ratio and y be the 3rd term

11.25/x=y     This means the fourth term divided by the common ratio will get the third term
20x=y           This means the second term multiplied by the common ratio will get the third term

11.25/x=20x        Set the two y's equal to each other, and solve for x!
20x^2=11.25
x^2=.5625
x=+-√.5625
x=.75 or -.75

Answer 2

__ , 20, __, 11.25

11.25 = 20 * r^(3-1)
11.25/20 = r^2
0.5625 = r^2
sqrt 0.5625 = r
0.75 = r...so common difference is 0.75 or 3/4