First-order linear recurrence relations t_(n+1) = r t_n + d: generating terms, long-term behaviour and the steady state d/(1 − r)

What this note covers

1. Interpret a linear recurrence step by step
2. Derive and test the steady state
3. Explain convergence through distance from equilibrium
4. Classify long-term behaviour by r
5. Model retention plus input in context
6. Keep equilibrium separate from an infinite series

6 sections · 10 key terms & formulas · 6 common mistakes