Practice Solving Linear Homogeneous Recurrence Equations – Part Ii (15) - Solving Linear Homogeneous Recurrence Equations – Part II

Practice: Solving Linear Homogeneous Recurrence Equations – Part II

Lesson 15Solving Linear Homogeneous Recurrence Equations – Part II

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9 questions

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6 sample questions

Question 1.
Define a linear homogeneous recurrence equation.
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Think about how sequences can be defined.
Question 2.
What are characteristic roots?
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Consider the roots of the equations from your algebra.
3Question 3.
What happens when roots of a characteristic equation are repeated?
- Only one solution exists
- The solution requires additional polynomial terms
- No solution exists
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Consider how sequences work with the same input.
4Question 4.
True or False? Initial conditions can determine the unique sequence from a recurrence relation.
- True
- False
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Think about the role of conditions in forming a solution.
Question 5.
Create a linear homogeneous recurrence relation of degree 4 with at least two repeated roots. Provide the characteristic polynomial and general solution.
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Look for characteristic roots through polynomial factoring.
Question 6.
Given that $a_n = 2a_{n-1} + a_{n-2}$ has initial conditions (0, 1), what is the specific sequence?
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Substituting the initial conditions helps find constants in the general solution.

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