Finite Differences

Spotting quadratics in data

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• A quadratic sequence has constant second differences, equal to 2a.
• Use the differences to recover a, then b and c from the first terms.
• Degree-d polynomials have constant d-th differences.

Steps

1. Differences of differences
2. Next in line
3. Fit the formula
4. Going further
5. Pentagonal numbers
6. Slicing a pizza