Final answer:
The given sequence follows a pattern of alternating between negative and positive terms by raising 2 to the power of n and multiplying by -1 raised to the power of n. The next three terms in the sequence are -32, 32, and -64.
Step-by-step explanation:
The given sequence is: -2, 4, -8, 16, ...
To generate each term, we can observe that the pattern alternates between negative and positive terms. The first term, -2, is obtained by raising 2 to the power of 1 and then multiplying by -1. The second term, 4, is obtained by raising 2 to the power of 2. The third term, -8, is obtained by raising 2 to the power of 3 and then multiplying by -1. In general, the nth term can be generated by raising 2 to the power of n and then multiplying by -1 raised to the power of n.
Using this pattern, the next three terms are:
-2^(5) = -32
32
-2^(6) = -64