Question

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?

Answer 1

t2=ar^(2-1)

20=ar

then

t4=ar^(4-2)

45/4=ar.r

45/4=20.r

45/80=r

Answer 2

r=±0.75

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!