Practice Proof Of Theorem - Part 1 (14.7) - Solving Linear Homogenous Recurrence Equations – Part I

Practice: Proof of Theorem - Part 1

Lesson 14.7Solving Linear Homogenous Recurrence Equations – Part I

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6 sample questions

Question 1.
Write the general form of a linear homogeneous recurrence relation of degree 2.
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Think about how each term relates to the previous ones.
Question 2.
What is meant by characteristic roots?
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Reflect on where they come from.
3Question 3.
What form does a linear homogeneous recurrence equation typically take?
- T(n) = a + b
- T(n) = a*T(n-1) + b*T(n-2)
- T(n) = a*T(n-2) + b*T(n-3)
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Look for how previous terms in the sequence appear.
4Question 4.
True or False: The characteristic roots of a recurrence equation can be the same.
- True
- False
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Consider the nature of quadratic equations.
Question 5.
For T(n) = 4T(n-1) - 4T(n-2), derive the characteristic equation and roots. Then find a general solution.
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Follow the steps to construct your polynomial from the recurrence relation.
Question 6.
Given the initial conditions T(0)=2, T(1)=3, find specific constants A and B for T(n) = A * 3^n + B * 1^n.
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Set up simultaneous equations based on initial terms.

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