Practice Proof Of Theorem - Part 2 (14.8) - Solving Linear Homogenous Recurrence Equations – Part I

Practice: Proof of Theorem - Part 2

Lesson 14.8Solving Linear Homogenous Recurrence Equations – Part I

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9 questions

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6 sample questions

Question 1.
What is the general form of a linear homogeneous recurrence relation?
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Look for the structure where the n-th term relates to its predecessors.
Question 2.
Define characteristic roots in the context of recurrence relations.
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Think about how these roots connect to the structure of the recurrence.
3Question 3.
What does the characteristic equation help us identify?
- The first term of the sequence
- The characteristic roots
- The final term of the sequence
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Recall its purpose in the solution process.
4Question 4.
True or False: All roots in a characteristic equation must be distinct.
- True
- False
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Consider instances where roots overlap.
Question 5.
Consider the recurrence relation S(n) = 2 * S(n-1) + 3 * S(n-2) with S(0) = 1 and S(1) = 4. Find the characteristic roots and derive the general form of the solution.
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Start with the characteristic equation before substituting in initial conditions.
Question 6.
Given a recursion with repeated roots, S(n) = S(n-1) + S(n-2) with initial conditions S(0) = 1 and S(1) = 1, show how you would find the nth term.
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Make sure to label your roots correctly when handling repeated instances.

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