–4, 8, –16, 32, . . .
A. arithmetic, 64, 128, 256
B. geometric, –64, 128, –256
C. geometric, –48, 64, –80
D. The sequence is neither geometric nor arithmetic.
The given sequence is not an arithmetic sequence because the difference between consecutive terms is not the same.
To determine if it is a geometric sequence, we can check if the ratio of consecutive terms is the same.
Ratio of 8 to -4 is -2.
Ratio of -16 to 8 is -2.
Ratio of 32 to -16 is -2.
Thus, the sequence is a geometric sequence with a common ratio of -2.
Therefore, the answer is (B) geometric, –64, 128, –256.