SEQ011 · Sequences & series · Classes 11–12
Recursive sequences
A recursive sequence defines each term from the term before it, starting from a given first term.
aₙ₊₁ = f(aₙ)Recursive sequences
📐 Formula
aₙ₊₁ = k·aₙ + c, a₁ given
✏️ Worked example
a₁ = 1, aₙ₊₁ = 2aₙ + 1: 1, 3, 7, 15, 31, 63 (Tower of Hanoi moves).
🌍 Where it is used
Loans with monthly interest and payment; computer loops.
❓ Quick check
a₁ = 2, aₙ₊₁ = aₙ + 5. a₃ = ?
🏋️ Practice
Easya₁ = 3, aₙ₊₁ = 2aₙ. List 4 terms.
Answer: 3, 6, 12, 24
Mediuma₁ = 10, aₙ₊₁ = aₙ − 4. a₅ = ?
Answer: −6
ChallengeWrite 1, 4, 13, 40 recursively.
Answer: a₁ = 1, aₙ₊₁ = 3aₙ + 1