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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a linear homogeneous recurrence equation?
💡 Hint: Think of the Fibonacci sequence.
Question 2
Easy
Identify the characteristic equation for T(n) = 3T(n-1) + 2T(n-2).
💡 Hint: Follow the structure of r^2 - ar - b.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
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
💡 Hint: Look for terms that rely only on previous values.
Question 2
True or False: The characteristic equation provides the exact solution to the recurrence relation.
- True
- False
💡 Hint: Think about what other information is needed.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Solve the recurrence relation T(n) = 3*T(n-1) - T(n-2) with T(0) = 5 and T(1) = 10. Demonstrate the steps.
💡 Hint: Remember to use the quadratic formula!
Question 2
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.
💡 Hint: Factor or use the quadratic formula for the eigenvalues!
Challenge and get performance evaluation