Question

The successive differences of a sequence are shown in this image. What is the degree of its associated polynomial expression? (1 point)

Answer 1

To determine the degree of the polynomial associated with a sequence based on its successive differences, you would typically follow these steps:

1. **Calculate the First Differences**: Find the differences between consecutive terms of the sequence.

2. **Calculate the Second Differences**: Find the differences between the first differences.

3. **Continue Calculating Differences**: Keep calculating successive differences until you reach a level of differences that are constant.

4. **Determine the Degree**: The degree of the polynomial is equal to the number of times you need to take differences until you reach a constant value.

If you have the successive differences from an image, you would ideally look for the first level of differences that are constant.

- If the first differences are constant, the degree is 1 (linear polynomial).
- If the second differences are constant, the degree is 2 (quadratic polynomial).
- If the third differences are constant, the degree is 3 (cubic polynomial).
- And so on.

Without the specific numbers from the image, I cannot provide a definitive answer, but you can follow this process with the actual data from the image to find the polynomial degree.