13.7. Examples of Linear Homogeneous Recurrence Equations

Try these first

1. 1.

   Define a recurrence equation.

   Hint

   Think about sequences and how they are defined.

2. 2.

   What is the Fibonacci sequence?

   Hint

   Recall the classic example often introduced first in math discussions.

3. 3.

   What does a recurrence equation define?

   • A sequence
   • A polynomial
   • A division
   • A matrix

   Hint

   Think about how sequences are structured.

4. 4.

   True or False: A non-homogeneous recurrence equation has no external addition.

   • True
   • False

   Hint

   Consider the impact of added terms.

5. 5.

   Create a non-homogeneous recurrence relation and solve it. Provide initial conditions.

   Hint

   Look for patterns as you calculate a few terms.

6. 6.

   Define a recurrence equation of degree 3 and describe how many initial conditions you would need to solve it.

   Hint

   Recall how the degree relates to the number of initial conditions.