Practice Recap Of Last Lecture (15.1) - Solving Linear Homogeneous Recurrence Equations – Part II

Practice: Recap of Last Lecture

Lesson 15.1Solving Linear Homogeneous Recurrence Equations – Part II

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6 sample questions

Question 1.
Define a linear homogeneous recurrence equation.
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Think about sequences like Fibonacci.
Question 2.
What is the purpose of the characteristic equation?
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It helps us find the roots related to the recurrence relation.
3Question 3.
Which of the following is true about the characteristic equation?
- It is unrelated to the recurrence relation.
- It helps identify the roots needed to determine solutions.
- It is always quadratic.
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Think about its role in helping form sequences.
4Question 4.
True or False: All roots of a characteristic polynomial must be distinct.
- True
- False
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Consider cases with Fibonacci-like sequences.
Question 5.
Consider the recurrence relation T(n) = T(n-1) + 2T(n-2). Find the characteristic roots and solve the equation. Discuss what happens when modifying coefficients.
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Factor the characteristic polynomial.
Question 6.
Create your own recurrence relation with at least one repeated root. Solve for the nth term and explain your steps.
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Focus on the polynomial degree based on root multiplicities.

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