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3 cards from this section. Quick, good the night before a test.
What is a linear homogeneous recurrence equation?
Think about how these equations relate sequences.
What do characteristic roots represent?
What do we derive from the characteristic equation?
What do we call the values derived from the characteristic polynomial of a recurrence relation?
Think about what those values represent.
True or False: Initial conditions are not necessary for determining unique solutions in recurrence equations.
Consider multiple sequences that can satisfy a recurrence.
Consider the recurrence relation a_n = 2a_{n-1} - a_{n-2}. Find and characterize its general solution.
Identify the polynomial from the given recursion.
Given the initial conditions a_0 = 3 and a_1 = 5, what coefficients α_1 and α_2 satisfy this in the previous multiple root example?
Substituting initial conditions helps find unknown constants.
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