The recursive formula for the geometric sequence is given as follows:
D.
- [tex]a_n = a_{n-1} \times \left(-\frac{1}{3}\right)[/tex]
What is a geometric sequence?
A geometric sequence is a sequence in which the result of the division of consecutive terms is always the same, called common ratio q.
The nth term of a geometric sequence is given by:
[tex]a_n = a_1q^{n-1}[/tex]
In which [tex]a_1[/tex] is the first term.
With a recursive formula, it is given by:
[tex]a_n = a_{n-1} \times q[/tex]
For this problem, the first term and the common ratio are:
[tex]a_1 = 9, q = -\frac{1}{3}[/tex]
Then the recursive formula is:
D.
- [tex]a_n = a_{n-1} \times \left(-\frac{1}{3}\right)[/tex]
More can be learned about geometric sequences at https://brainly.com/question/11847927
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