Question

the successive differences of a sequence are shown in this imagine what is the degree of its associated polynomial expression

Answer 1

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

1. **List the first differences**: Compute the differences between consecutive terms of the sequence. This is the first difference.

2. **Continue finding differences**: Take the differences of the first differences to get the second differences, then the third differences, and so on.

3. **Identify when differences stabilize**: The degree of the polynomial is equal to the number of times you need to compute differences until you reach a row of differences that are constant (do not change anymore).

For example:
- If the first differences are not constant but the second differences are constant, the polynomial is of degree 2.
- If the second differences are not constant but the third differences are constant, the polynomial is of degree 3, and so on.

If you provide the values of the sequence, I can assist you in determining the degree of the associated polynomial.