Given the explicit formula for the Geometric Sequence:
[tex]a_n=9\cdot(-\frac{1}{3})^{(n-1)}[/tex]
Where the nth term is:
[tex]a_n[/tex]
Then, you need to remember that, by definition, the Recursive Formula for a Geometric Sequence has this form:
[tex]a_n=a_{n-1}\cdot r[/tex]
Where "r" is the common ratio.
In this case, having the explicit formula with the form:
[tex]a_n=a_1\cdot r^{(n-1)}[/tex]
You can identify that:
[tex]r=-\frac{1}{3}[/tex][tex]a_1=9[/tex]
Therefore, you can set up the following recursive formula:
[tex]a_n=a_{n-1}(-\frac{1}{3})[/tex]
Hence, you get:
[tex]\begin{cases}a_1=9_{} \\ \\ a_n=a_{n-1}(-\frac{1}{3})\end{cases}[/tex]
Therefore, the answer is: Option A.
