Practice Extension To Degree K Linear Homogeneous Recurrence Equations (14.9)

Practice: Extension to Degree k Linear Homogeneous Recurrence Equations

Lesson 14.9Solving Linear Homogenous Recurrence Equations – Part I

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8 questions

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6 sample questions

Question 1.
What is the general form of a linear homogeneous recurrence equation?
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Think about how each term relates to the previous terms.
Question 2.
Define a characteristic equation.
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Consider what replacing A_n with λ^n does.
3Question 3.
What does the characteristic equation reveal?
- Roots of the sequence
- Initial conditions
- Terms of the sequence
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Think about what you are solving with that equation.
4Question 4.
Is it possible to have multiple sequences satisfying the same recurrence relation?
- True
- False
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Consider how initial conditions relate to the uniqueness of a solution.
Question 5.
Given a recurrence relation A_n = 5A_{n-1} - 6A_{n-2}, derive its general solution and illustrate how the initial conditions would affect the constants.
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Find roots, set general form, and plug in initial conditions.
Question 6.
Analyze the recurrence given by A_n = A_{n-1} + 2A_{n-2} and identify if there are specific cases for constant definitions based on roots.
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Solve the quadratic and understand how roots affect the sequence structure.

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