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 rat
io in this sequence?
2 answers:
Answer:
t2=ar^(2-1)
20=ar
then
t4=ar^(4-2)
45/4=ar.r
45/4=20.r
45/80=r
Answer:
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!
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