Question

12
29
56
93
140
17
27
37
47
10
10
10
0
0
The successive differences of a sequence are shown in this image. What is the degree of its
associated polynomial expression?

Answer 1

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**.