–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
C) geometric, -48, 64, -80
To determine if the sequence is arithmetic or geometric, we look at the differences or ratios between consecutive terms.
-4 to 8: 8 - (-4) = 12
8 to -16: -16 - 8 = -24
-16 to 32: 32 - (-16) = 48
Since the differences between consecutive terms are not constant, the sequence is not arithmetic.
8 ÷ -4 = -2
-16 ÷ 8 = -2
32 ÷ (-16) = -2
Since the ratios between consecutive terms are all the same (-2), the sequence is geometric. The next terms would be calculated as:
32 * -2 = -64
-64 * -2 = 128
128 * -2 = -256
Therefore, the correct answer is C) geometric, -48, 64, -80.