To determine the degree of the associated polynomial expression of a sequence based on its successive differences, we can look at the differences provided:
1st differences:
- 12, 29, 56, 93, 140
- The differences here are:
- 29 - 12 = 17
- 56 - 29 = 27
- 93 - 56 = 37
- 140 - 93 = 47
This gives us the 1st differences: 17, 27, 37, 47.
2nd differences:
- 27 - 17 = 10
- 37 - 27 = 10
- 47 - 37 = 10
This gives us a constant 2nd difference of 10.
Since the 2nd differences are constant, this indicates that the original sequence can be modeled by a polynomial of degree 2.
Hence, the degree of the associated polynomial expression for the given sequence is 2.