Question

complete the table
x , y
1,9
2,6
3,5
4,7
5, ?

Answer 1

The missing value is 13.

Using finite differences:
y: 9, 6, 5, 7, ?
1st diffs: -3, -1, 2, ?
2nd diffs: 2, 3, ?
3rd diffs: 1 (constant for a cubic)

Assume the 3rd difference stays 1, so next 2nd diff = 3+1 = 4, next 1st diff = 2+4 = 6, so next y = 7+6 = 13.

Completed table:
1, 9
2, 6
3, 5
4, 7
5, 13