The second term in a geometric sequence is 20. The fourth term in the same sequence is 45/4 or 11.25. What is the common ratio in this sequence.

3/4

Step-by-step explanation:

We know a geometric sequence has the formula:  a_n = a_1 * r^(n-1)

a_2 = 20

a_4 = (45/4)

so...    a_2 = a_1* r^(2-1) =  20

and    a_4 = a_1* r^(4-1) = (45/4)

a_1 * r = 20

a_1* r^3 = (45/4)

a_1 = 20/r

(20/r) * r^3 = (45/4)

20 * r*r = 45/4

r*r = 45/80 =  9/16

r =  3/4   or  r = -3/4   it must be positive.

common ratio is r = 3/4

step-by-step explanation:

you can add the two numbers and divide the result by 2. or you can find the gap between the two numbers and add half of this to the smaller number.