Answer:
The sequence is not a geometric sequence
Step-by-step explanation:
In a geometric sequence you find the following term multiplying the current by a fixed quantity called the common ratio.
To prove if a sequence is geometric we need to check if the ratio is consistent across the sequence. To check for the ratio we use the formula:
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
were
[tex]r[/tex] is the ratio
[tex]a_n[/tex] is the current term
[tex]a_{n-1}[/tex] is the previous term
Let's star with 1, so [tex]a_n=1[/tex] and [tex]a_{n-1}=-1[/tex]
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
[tex]r=\frac{1}{-1}[/tex]
[tex]r=-1[/tex].
Now let's check 4 and 1, so [tex]a_n=4[/tex] and [tex]a_{n-1}=1[/tex]
[tex]r=\frac{a_n}{a_{n-1}}[/tex]
[tex]r=\frac{4}{1}[/tex]
[tex]r=4[/tex]
Since the ratios between two pair of numbers are different, we can conclude that the sequence is not geometric.
