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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Write the general form of a linear homogeneous recurrence relation of degree 2.
💡 Hint: Think about how each term relates to the previous ones.
Question 2
Easy
What is meant by characteristic roots?
💡 Hint: Reflect on where they come from.
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 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)
💡 Hint: Look for how previous terms in the sequence appear.
Question 2
True or False: The characteristic roots of a recurrence equation can be the same.
- True
- False
💡 Hint: Consider the nature of quadratic equations.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
For T(n) = 4T(n-1) - 4T(n-2), derive the characteristic equation and roots. Then find a general solution.
💡 Hint: Follow the steps to construct your polynomial from the recurrence relation.
Question 2
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.
💡 Hint: Set up simultaneous equations based on initial terms.
Challenge and get performance evaluation