Answer:
-4 * 3^(n-1)
Explanation:
The rule for a geometric sequence is given by the formula an = a1 * r^(n-1), where a1 is the first term, r is the common ratio, and n is the term number. To find the common ratio, we can use the formula r = a2/a1 = a3/a2, since any two consecutive terms in a geometric sequence have the same ratio.
Given that a3 = -12 and r = 3, we can solve for a1 as follows:
a3 = a1 * r^(3-1)
-12 = a1 * 3^2
a1 = -4
Therefore, the rule for this geometric sequence is an = -4 * 3^(n-1).