MEPX
Chapter 3 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 3 of 10

Geometric sequences

Multiplying by the same amount.

The form

Each term is the previous one times a constant ratio. 2, 6, 18, 54 triples each step, and the nth term is the first times the ratio to the power n minus one.

  • A ratio above 1 grows explosively; between 0 and 1 it decays towards zero.
  • Compound interest, population growth and radioactive decay are all geometric.

Infinite sums

If the ratio is between -1 and 1, adding infinitely many terms gives a finite total. That is why a half plus a quarter plus an eighth and so on approaches exactly one.