MEPX
Chapter 6 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 6 of 10

Writing the nth term

From a list to a formula.

Linear rules

With a constant difference d, the rule is d times n plus an adjustment. Work out d, multiply by n, then compare with the actual first term to find the adjustment.

  • 3, 7, 11, 15 has d of 4, and 4n gives 4, 8, 12, so the rule is 4n minus 1.
  • Substituting n equals 1 should always return the first term.

Quadratic rules

A constant second difference means an n squared term, and half that second difference is its coefficient. Subtract that part and what remains is a linear rule you already know how to find.