Practice Solving Linear Homogenous Recurrence Equations – Part I (14) - Solving Linear Homogenous Recurrence Equations – Part I

Practice: Solving Linear Homogenous Recurrence Equations – Part I

Lesson 14Solving Linear Homogenous Recurrence Equations – Part I

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10 questions

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6 sample questions

Question 1.
State the general form of a linear homogeneous recurrence equation.
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Consider the structure of sequences based on previous terms.
Question 2.
What does the term 'characteristic roots' refer to?
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Think of how these roots help define the terms of the sequence.
3Question 3.
What is the general form of a linear homogeneous recurrence relation?
- a_n = c_1 a_{n-1} + c_2 a_{n-2}
- a_n = c_1 a_{n-1} + c_2 a_{n-2} + c_3
- a_n = c_1 + c_2 a_{n-2}
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Focus on the dependency of terms on previous terms.
4Question 4.
True or False: The characteristic equation for degree two always has two distinct roots.
- True
- False
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Consider the properties of quadratic equations.
Question 5.
Consider a recurrence relation $a_n = 2a_{n-1} + 3a_{n-2}$ with a(0) = 4, a(1) = 5. Determine a closed form for a_n.
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Focus on solving the characteristic equation and then using initial conditions.
Question 6.
Prove that the sequence defined by $F_n = F_{n-1} + F_{n-2}$ indeed generates the Fibonacci series.
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Base cases are key, then follow with cases n >= 2.

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