Answer:
A geometric series a geometric sequence.
Step-by-step explanation:
Given sequence is :
[tex]-\frac{1}{3},\frac{1}{6},-\frac{1}{12},\frac{1}{24},-\frac{1}{48}[/tex]
We will check the nature of given sequence:
Firstly find the common difference
[tex]\frac{1}{6}-(-\frac{1}{3})=-\frac{1}{12}-\frac{1}{6}[/tex]
[tex]\frac{1}{2}\neq -\frac{1}{4}[/tex]
So, its not a arithmetic sequence.
Now check for geometric sequence.
Find the common ratio
[tex]\frac{\frac{1}{6} }{-\frac{1}{3} }=\frac{-\frac{1}{12} }{\frac{1}{6} }[/tex]
[tex]-\frac{1}{2}=-\frac{1}{2}[/tex]
So, a geometric series a geometric sequence.
That's the final answer.
