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3 cards from this section. Quick, good the night before a test.
What is the characteristic equation for a_n = 4a_{n-1} + 4a_{n-2}?
Derive the equation based on the recurrence relation.
Define a homogeneous recurrence relation.
Think about the form of the equation.
What type of equation derives from a linear homogeneous recurrence relation?
Remember the definition of a characteristic equation.
True or false: Repeated roots require polynomial terms multiplied by n.
Think about how repeated roots modify the general solution.
Given a recurrence relation a_n = -2a_{n-1} - 5a_{n-2}; find and analyze the characteristic roots.
Use the quadratic formula to find the roots.
Consider the recurrence relation a_n = a_{n-1} + a_{n-2} with initial conditions a_0 = 2, a_1 = 3. Find the specific sequence.
You can set up equations from known initial values to solve for the sequence coefficients.
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