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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is a characteristic equation?
💡 Hint: Think of how we find solutions to polynomials.
Question 2
Easy
Define distinct roots in the context of recurrence relations.
💡 Hint: What would happen if roots were the same?
Practice 3 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 the general form of a recurrence relation with two distinct roots?
- a_n = α₁r₁ⁿ + α₂r₂ⁿ
- a_n = α(r₁ + r₂)ⁿ
- a_n = (r₁ + r₂)ⁿ
💡 Hint: Remember the format with constants.
Question 2
True or False: Distinct roots result in a unique sequence for any initial values.
- True
- False
💡 Hint: Recall how distinct roots behave.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the recurrence relation a_n = 5a_{n-1} - 6a_{n-2}, find the characteristic roots and express the general solution.
💡 Hint: Think about how to factor the quadratic equation.
Question 2
Derive the general term for a recurrence relation a_n = a_{n-1} + a_{n-2} with given initial conditions a_0 = 1, a_1 = 1.
💡 Hint: Remember to equate using the initial conditions.
Challenge and get performance evaluation