Recurrence Relations Defined

Combinatorics · Axiom Academy

LESSON Recurrence Relations Defined Understanding the formal definition and classification of recurrence relations 1. Definition and Initial Conditions A recurrence relation for the sequence a n is an equation that expresses a n in terms of one or more previous terms. The equation must specify initial conditions to uniquely determine the sequence. 2. Order of a Recurrence Relation The order (or degree) of a recurrence relation is the difference between the highest and lowest indices that appear in the relation. It tells us how many previous terms are needed to compute the next term. 3. Homogeneous vs. Nonhomogeneous This classification depends on whether the recurrence contains terms that don't involve the sequence itself. 4. Linear vs. Nonlinear and Constant Coefficients These properties determine which solution techniques we can apply.

This is the written version of the interactive lesson above. See the full Combinatorics course.