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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 equation of degree 2.
💡 Hint: Consider how n-th term relates to its previous terms.
Question 2
Easy
What is the Fibonacci recurrence relation?
💡 Hint: Look at how each term is generated from the two previous terms.
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 is a linear homogeneous recurrence relation?
💡 Hint: Recall the general form presented in class.
Question 2
True or False: The characteristic equation is always a quadratic for degree 2 recurrence relations.
- True
- False
💡 Hint: Think about the degree of the recurrence.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the recurrence relation a_n = 4a_{n-1} - 4a_{n-2} with initial conditions a_0 = 2 and a_1 = 10, find the explicit formula and calculate a_2.
💡 Hint: Substitute n = 0 and n = 1 into the general form to create equations.
Question 2
Analyze the recurrence relation a_n = a_{n-1} + a_{n-2} and prove that it behaves like the Fibonacci sequence.
💡 Hint: Look at how each term forms by summing the two preceding terms.
Challenge and get performance evaluation