Question

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.

Answer 1

3/4

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