Question

What are the 2nd differences of the polynomial sequence shown in the table?

Answer 1

To determine the 2nd differences of a polynomial sequence, we need to find the differences of the differences.

Looking at the table, we can see that the sequence is:

Term 1: 1
Term 2: 6
Term 3: 17
Term 4: 34
Term 5: 57

To find the 1st differences, we subtract each term from its consecutive term:
6 - 1 = 5
17 - 6 = 11
34 - 17 = 17
57 - 34 = 23

To find the 2nd differences, we subtract each 1st difference from its consecutive 1st difference:
11 - 5 = 6
17 - 11 = 6
23 - 17 = 6

Therefore, the 2nd differences of the polynomial sequence are all 6.