Practice - Definition of Linear Homogeneous Recurrence Equations
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
Write the general form of a linear homogeneous recurrence equation of degree 2.
💡 Hint: Consider how n-th term relates to its previous terms.
What is the Fibonacci recurrence relation?
💡 Hint: Look at how each term is generated from the two previous terms.
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What is a linear homogeneous recurrence relation?
💡 Hint: Recall the general form presented in class.
True or False: The characteristic equation is always a quadratic for degree 2 recurrence relations.
💡 Hint: Think about the degree of the recurrence.
Get performance evaluation
Challenge Problems
Push your limits with advanced challenges
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.
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.