Final answer:
The recursive formula for the geometric sequence -1.5, 6, -24, 96 is a1 = -1.5, an = -4 * a(n-1) for n > 1, with a common ratio of -4.
Step-by-step explanation:
To complete the recursive formula of the geometric sequence -1.5, 6, -24, 96, we need to determine the common ratio between the terms. By dividing any term by its preceding term, we can find the ratio. In this case:
6 / (-1.5) = -4
(-24) / 6 = -4
96 / (-24) = -4
Since the ratio is consistent, it's clear that the common ratio (r) is -4.
A recursive formula also needs a starting value, which is the first term of the sequence. For this sequence, the starting value (a1) is -1.5. Thus, the recursive formula for the given geometric sequence can be written as:
a1 = -1.5
an = -4 * an-1 (for n > 1)