The sequence that is a geometric sequence is:
-1, 4, 16, 64
To determine if a sequence is geometric, you need to check if there is a common ratio between consecutive terms. In a geometric sequence, each term after the first is found by multiplying the previous term by a fixed, non-zero number.
Let's calculate the ratios for each sequence:
1. For the sequence -2, 10, 18, 30:
- The ratios are: 10 / (-2) = -5, 18 / 10 = 1.8, 30 / 18 = 1.67
- Since the ratios are not the same, this is not a geometric sequence.
2. For the sequence -3, 6, 12, 24:
- The ratios are: 6 / (-3) = -2, 12 / 6 = 2, 24 / 12 = 2
- Since the ratios are the same (2), this is a geometric sequence.
3. For the sequence -1, 4, 16, 64:
- The ratios are: 4 / (-1) = -4, 16 / 4 = 4, 64 / 16 = 4
- Since the ratios are the same (4), this is a geometric sequence.
4. For the sequence -4, -1, 2, 5:
- The ratios are: -1 / (-4) = 0.25, 2 / (-1) = -2, 5 / 2 = 2.5
- Since the ratios are not the same, this is not a geometric sequence.
Therefore, the sequence -1, 4, 16, 64 is the geometric sequence as it has a common ratio of 4 between consecutive terms.
