Answer:
1/2
Explanation:
Given a geometric progression with the following:
• The first term, a= -8
,
• The 6th term = -1/4
The nth term of a geometric progression is obtained using the formula:
[tex]\begin{gathered} U_n=ar^{n-1}\text{ where:} \\ a=\text{first term} \\ r=\text{common ratio} \end{gathered}[/tex]
Substitute the given values:
[tex]U_6=(-8)\times r^{6-1}=-\frac{1}{4}[/tex]
We solve the equation for r:
[tex]\begin{gathered} -8r^5=-\frac{1}{4} \\ \text{Divide both sides by -8} \\ \frac{-8r^5}{-8}=-\frac{1}{4\times-8} \\ r^5=\frac{1}{32} \end{gathered}[/tex]
Next, take the 5th root of both sides:
[tex]\begin{gathered} \sqrt[5]{r^5}=\sqrt[5]{\frac{1}{32}} \\ r=\frac{1}{2} \end{gathered}[/tex]
The common ratio of the geometric progression is 1/2.
