Answer:
The common ratio to the given geometric sequence is [tex]-\frac{1}{3}[/tex]
Therefore common ratio is [tex]r=-\frac{1}{3}[/tex]
Step-by-step explanation:
Given sequence is 9,-3,1,[tex]-\frac{1}{3}[/tex]
Given that the given sequence is a geometric sequence
To find the common ratio of the given sequence :
Let [tex]a_1=9,a_2=-3,a_3=1,a_4=-\frac{1}{3}[/tex]
Common ratio [tex]r=\frac{a_2}{a_1}[/tex]
Substitute [tex]a_1=9,a_2=-3[/tex]
[tex]r=\frac{-3}{9}[/tex]
[tex]=-\frac{1}{3}[/tex]
Therefore [tex]r=-\frac{1}{3}[/tex]
Common ratio [tex]r=\frac{a_3}{a_2}[/tex]
Substitute [tex]a_3=1,a_2=-3[/tex]
[tex]r=\frac{1}{-3}[/tex]
Therefore [tex]r=-\frac{1}{3}[/tex]
The common ratio to the given geometric sequence is [tex]-\frac{1}{3}[/tex]
Therefore common ratio is [tex]r=-\frac{1}{3}[/tex]
