About this topic
Before you begin
Solve first- and second-order linear recurrences, including those reduced by a given substitution, analyse their long-term behaviour and model with them.
Learning goals
- Solve first-order linear recurrence relations with constant coefficients
- Solve second-order linear homogeneous recurrence relations with constant coefficients
- Analyse the long-term behaviour of a sequence defined by a recurrence
- Formulate and interpret recurrence-relation models
Syllabus statements covered
- Include: behaviour of a sequence, such as the limiting behaviour of a sequence; solution of (i) first order linear (homogeneous and non-homogeneous) recurrence relations with constant coefficients of the form uₙ = auₙ₋₁ + b, a, b ∈ ℝ, a ≠ 0; (ii) second order linear homogeneous recurrence relations with constant coefficients including those that can be transformed to the above by means of a given substitution; modelling with recurrence relations of the forms above.
Choose a lesson
Work through them in order.
- Not startedLinear recurrence relationsNextSolve first-order relations through their fixed point and second-order relations through their characteristic equation, then model with them.
- Not startedRecurrences solved by substitutionNextUse a given substitution to turn a recurrence into a linear second-order relation, solve it and return to the original sequence.