MEPX
Chapter 4 of 10All chapters
  1. 1Finding the rule
  2. 2Arithmetic sequences
  3. 3Geometric sequences
  4. 4Sequences worth knowing
  5. 5Primes and factors
  6. 6Writing the nth term
  7. 7Patterns from shapes
  8. 8Recursive rules
  9. 9Patterns outside mathematics
  10. 10Solving pattern puzzles

Chapter 4 of 10

Sequences worth knowing

The ones that keep appearing.

The short list

Squares 1, 4, 9, 16. Cubes 1, 8, 27. Triangular numbers 1, 3, 6, 10. Powers of two 1, 2, 4, 8. Fibonacci 1, 1, 2, 3, 5, 8.

  • Triangular numbers count handshakes and connections in a group.
  • Powers of two run through computing, from bytes to binary search.

Fibonacci

Each term is the sum of the two before it. The ratio between consecutive terms settles towards the golden ratio, roughly 1.618, which shows up in growth patterns.