This sequence alternates between positive and negative terms, and it appears to follow a geometric progression where each term is multiplied by $-\frac{1}{2}$ to get the next term.

Let's verify by dividing each consecutive term by the previous one:

$\frac{-256}{512} = -\frac{1}{2}$ $\frac{128}{-256} = -\frac{1}{2}$ $\frac{-64}{128} = -\frac{1}{2}$

Since the common ratio is $-\frac{1}{2}$, we can find the next three terms by multiplying the last term, $-64$, by $-\frac{1}{2}$ repeatedly:

1. $-64 \times -\frac{1}{2} = 32$
2. $32 \times -\frac{1}{2} = -16$
3. $-16 \times -\frac{1}{2} = 8$

Thus, the next three terms are: 32, -16, and 8.

The correct answer is: 32, -16, and 8.

Would you like further clarification or details on this sequence? Here are 5 related questions to expand your understanding:

1. What is the general formula for the nth term of a geometric sequence?
2. How do you determine the common ratio of a geometric sequence?
3. Can a geometric sequence have a positive common ratio?
4. How would the sequence change if the common ratio were positive?
5. How do you determine the sum of an infinite geometric series?

Tip: In a geometric sequence, the ratio between consecutive terms remains constant.