Practice Theorem Statement (14.6) - Solving Linear Homogenous Recurrence Equations – Part I

Practice: Theorem Statement

Lesson 14.6Solving Linear Homogenous Recurrence Equations – Part I

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6 sample questions

Question 1.
Define a linear homogeneous recurrence equation.
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Look at how the n-th term is constructed from prior terms.
Question 2.
What is a characteristic equation?
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Recall how you form it from the recurrence relation.
3Question 3.
What form does the n-th term of a recurrence equation take when the roots are distinct?
- a_n = r^n
- a_n = αr_1^n + βr_2^n
- a_n = c_1 + c_2n
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Think about how we construct the sequence based on distinct roots.
4Question 4.
True or False: An initial condition can determine multiple sequences that fit a single recurrence relationship.
- True
- False
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Consider the implications of having the same starting point.
Question 5.
Given a recurrence relation with the characteristic equation $r^2 - 5r + 6 = 0$ , find the general form of the n-th term and particular values for $a_0 = 2$ , $a_1 = 3$ .
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Start by finding the roots, then use the initial terms in your general form.
Question 6.
Describe how the distinct roots could influence the behavior of a recurrence relation in terms of convergence.
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Comparing growth rates can help determine which terms will dominate as n increases.

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