MEPX
Chapter 1 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 1 of 10

Finding the rule

A checklist that solves most sequences.

Work through it in order

Look at the differences between terms first. If they are constant, the rule is linear. If not, look at the differences of those differences, then try ratios, then sums of previous terms.

  • Constant first difference means arithmetic: add the same each time.
  • Constant second difference means the rule involves n squared.

Check against every term

A rule that fits the first three terms and fails the fourth is not the rule. Always test it on all of them, including any given later in the list.