Final answer:
The level of difference that is constant for the sequence -2, 0, 14, 46, 102, 188 is the third level, indicating that it is a quadratic sequence.
Step-by-step explanation:
The student has asked to identify the level of difference for the sequence -2, 0, 14, 46, 102, 188. To do this, we calculate the differences between consecutive terms to find a pattern.
- First Level Differences: 0 - (-2) = 2, 14 - 0 = 14, 46 - 14 = 32, 102 - 46 = 56, 188 - 102 = 86
- Second Level Differences: 14 - 2 = 12, 32 - 14 = 18, 56 - 32 = 24, 86 - 56 = 30
- Third Level Differences: 18 - 12 = 6, 24 - 18 = 6, 30 - 24 = 6
From the third level, we can see that the differences are constant at 6, meaning that the sequence is quadratic. The level of difference that is constant is the third level.