Answer:
1/2
Explanation:
Given a certain sequence of number,
[tex]a_n[/tex]
The common ratio of the sequence is rhe ratio between two consecutive numbers of the sequence, namely:
[tex]r=\frac{a_{n+1}}{a_n}[/tex]
In this problem, the sequence contains the numbers:
-164, -82, -41, -20.5
We can calculate the common ratio by taking the 1st and 2nd number; we have:
[tex]a_n=-164\\a_{n+1}=-82[/tex]
Therefore, the common ratio is:
[tex]r=\frac{-82}{-164}=\frac{1}{2}[/tex]
And we can easily verify that this ratio is valid also for the other numbers in the sequence:
[tex]r=\frac{-41}{-82}=\frac{1}{2}\\r=\frac{-20.5}{-41}=\frac{1}{2}[/tex]
