Patterns to Formulas

Matchsticks and dot triangles

An interactive lesson with 7 steps, about 6 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 pattern growing by d each step has rule dn + (first term − d).
• Linear patterns lie on a straight line.
• Triangular numbers: n(n + 1)/2, found by pairing two copies.

Steps

1. A row of squares
2. Fifty squares
3. Find the rule
4. Which formula?
5. Triangles of dots
6. The 20th triangle
7. A zigzag of triangles