Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
State the general form of a linear homogeneous recurrence equation.
💡 Hint: Consider the structure of sequences based on previous terms.
Question 2
Easy
What does the term 'characteristic roots' refer to?
💡 Hint: Think of how these roots help define the terms of the sequence.
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 the general form of a linear homogeneous recurrence relation?
- a_n = c_1 a_{n-1} + c_2 a_{n-2}
- a_n = c_1 a_{n-1} + c_2 a_{n-2} + c_3
- a_n = c_1 + c_2 a_{n-2}
💡 Hint: Focus on the dependency of terms on previous terms.
Question 2
True or False: The characteristic equation for degree two always has two distinct roots.
- True
- False
💡 Hint: Consider the properties of quadratic equations.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a recurrence relation \( a_n = 2a_{n-1} + 3a_{n-2} \) with a(0) = 4, a(1) = 5. Determine a closed form for a_n.
💡 Hint: Focus on solving the characteristic equation and then using initial conditions.
Question 2
Prove that the sequence defined by \( F_n = F_{n-1} + F_{n-2} \) indeed generates the Fibonacci series.
💡 Hint: Base cases are key, then follow with cases n >= 2.
Challenge and get performance evaluation