Answer:
[tex]\frac{2}{3}[/tex] is the common ratio.
Step-by-step explanation:
We have been given the geometric sequence
[tex]18,12,8,\frac{16}{3}[/tex]
We need to find the common ratio:
[tex]\text{common ratio}=\frac{a_2}{a_1}[/tex]
Common ratio is the the ratio which is same between the consecutive numbers
Between 18 and 12[tex]a_2=12,a_1=18[/tex] on substituting the values in the formula we get:
[tex]\text{common ratio}=\frac{12}{18}=\frac{2}{3}[/tex]
Between 12 and 8[tex]a_2=8,a_1=12[/tex] on substituting the values in the formula we get:
[tex]\text{common ratio}=\frac{8}{12}=\frac{2}{3}[/tex]
Hence, we will get [tex]\frac{2}{3}[/tex] as common ratio.
