Answer: To find the rule for a geometric sequence, we need to determine the first term (a1) and the common ratio (r).
The given sequence is 64, -32, 16, -8. We can see that the first term is 64, and to get to the second term, we need to multiply the first term by -1/2. To get to the third term, we need to multiply the second term by -1/2, and so on.
So, the common ratio (r) is -1/2, since each term is obtained by multiplying the preceding term by -1/2.
The formula for the nth term (an) of a geometric sequence with first term a1 and common ratio r is:
an = a1 * r^(n-1)
Substituting the values we found, we get:
an = 64 * (-1/2)^(n-1)
Therefore, the rule for the given geometric sequence is:
an = 64 * (-1/2)^(n-1)
Explanation: