Practice General Method For Solving Recurrence Equations (14.3) - Solving Linear Homogenous Recurrence Equations – Part I

Practice: General Method for Solving Recurrence Equations

Lesson 14.3Solving Linear Homogenous Recurrence Equations – Part I

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6 sample questions

Question 1.
What is a linear homogeneous recurrence equation?
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Think of the Fibonacci sequence.
Question 2.
Identify the characteristic equation for T(n) = 3T(n-1) + 2T(n-2).
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Follow the structure of r^2 - ar - b.
3Question 3.
What form does a linear homogeneous recurrence equation take?
- T(n) = a*T(n-1) + b*T(n-2)
- T(n) = a*T(n-1) + b
- T(n) = an^2 + bn + c
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Look for terms that rely only on previous values.
4Question 4.
True or False: The characteristic equation provides the exact solution to the recurrence relation.
- True
- False
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Think about what other information is needed.
Question 5.
Solve the recurrence relation T(n) = 3*T(n-1) - T(n-2) with T(0) = 5 and T(1) = 10. Demonstrate the steps.
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Remember to use the quadratic formula!
Question 6.
Consider a sequence defined by T(n) = T(n-1) + 4*T(n-2) - T(n-3). How would you approach solving for T(n) using the characteristic equation? Present your method.
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Factor or use the quadratic formula for the eigenvalues!

5 more questions in this section. Enroll free to practise them all.