The explicit formula for the geometric sequence Negative one-ninth, one-third, negative 1, 3, negative 9, ellipsis is f (x) = negative one-ninth (negative 3) Superscript x minus 1. What is the common ratio and recursive formula for this sequence?

Common ratio, r=-3

Recursive Formula

Step-by-step explanation:

The formula for the geometric sequence: is given as:

Common Ratio

Dividing the next terms by the previous terms, we obtain:

Therefore, the common ratio of the sequence, r=-3

Recursive Formula

We observe that the next term, is obtained by the multiplication of the previous term. f(n-1) by -3.

Therefore, a recursive formula for the sequence is:

step-by-step explanation: