Final answer:
The recursive formula for the given geometric sequence [0.2, -1, 5, -25, ...] is an = an-1 * (-5), with the first term (a1) equal to 0.2.
Step-by-step explanation:
The given sequence [0.2, -1, 5, -25, ...] is a geometric sequence where each term is multiplied by a common ratio to get the next term. To find the recursive formula, we need to identify the first term and the common ratio. The first term (a1) is 0.2 and by dividing the second term by the first term, we can find the common ratio (r), which is -1 / 0.2 = -5.
The recursive formula for a geometric sequence is an = an-1 * r, where an is the nth term and an-1 is the previous term. In this case, the recursive formula is:
an = an-1 * (-5), with a1 = 0.2