The second termn in a geometric sequence is 20. The fourth termn in the same sequense is 45/4, or 11.225. What is the common ratio in this sequence?

t2=ar^ (2-1)

20=ar

then

t4=ar^ (4-2)

45/4=ar. r

45/4=20. r

45/80=r

r=±0.75

Step-by-step explanation:

Given:

a2 = 20

a4 = 45/4

As a geometric sequence has a common ratio and is given by:

an=a1 (r) ^n-1

where

an=nth term

a1=first term

n=number of term

r=common ratio

Now

a2=20=a1 (r) ^ (2-1)

20=a1 (r) ^1

20=a1*r

Also

a4=45/4=a1 (r) ^ (4-1)

45/4=a1r^3

(a1*r) r^2=45/4

Substituting value of 20=a1*r

(20) r^2=45/4

r^2=45/4 (20)

r^2=0.5625

r=±0.75!