Question

the second term in a geometric sequence is 12. the fourth term in the same sequencce is 4/3. what is the common ratio in this sequence?

Answer 1

geo is
an=a1r^(n-1)

2nd term is 12
4th term is 4/3

a2=a1r^(2-1)=12
a2=a1r=12

a4=a1r^(4-1)=4/3
a4=a1r^3=4/3

we have
a1r=12 and a1r^3=4/3
(a1r^3)/(a1r)=r^2=(4/3)/12=1/9

1/9=r^2
sqrt oth sides
1/3=r

the common ratio is 1/3