Final answer:
The recursive formula for the given geometric sequence is an = an-1 / (-2).
Step-by-step explanation:
The recursive formula for a geometric sequence is given by:
an = an-1 * r
where an is the nth term and r is the common ratio.
In this case, the explicit formula is an = 13 * (-2)^(n-1).
To find the recursive formula, we need to express the explicit formula in the form an = an-1 * r.
Let's divide both sides of the equation by -2 to isolate the term an-1:
an / (-2) = an-1
Therefore, the recursive formula is an = an-1 / (-2).