Practice Definition Of Linear Homogeneous Recurrence Equations (14.2) - Solving Linear Homogenous Recurrence Equations – Part I
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Definition of Linear Homogeneous Recurrence Equations

Practice - Definition of Linear Homogeneous Recurrence Equations

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Practice Questions

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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.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

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.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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.

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