Practice Theorem Statement For Distinct Roots (154) - Solving Linear Homogeneous Recurrence Equations – Part II

Practice: Theorem Statement for Distinct Roots

Lesson 154Solving Linear Homogeneous Recurrence Equations – Part II

Practise this section

7 questions

Flashcard drill
2 cards from this section. Quick, good the night before a test.
Exercise
5 questions · about 3 min · pass mark 70%. Hints available.
Sign up to start the exercise
Quiz
2 questions · about 1 min · pass mark 70%. Hints available.
Sign up to start the quiz

6 sample questions

Question 1.
What is a characteristic equation?
Show hintHide hint
Think of how we find solutions to polynomials.
Question 2.
Define distinct roots in the context of recurrence relations.
Show hintHide hint
What would happen if roots were the same?
3Question 3.
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
Show hintHide hint
Remember the format with constants.
4Question 4.
True or False: Distinct roots result in a unique sequence for any initial values.
- True
- False
Show hintHide hint
Recall how distinct roots behave.
Question 5.
Given the recurrence relation a_n = 5a_{n-1} - 6a_{n-2}, find the characteristic roots and express the general solution.
Show hintHide hint
Think about how to factor the quadratic equation.
Question 6.
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.
Show hintHide hint
Remember to equate using the initial conditions.

3 more questions in this section. Enroll free to practise them all.