14.1. Recap of Previous Lecture

Try these first

1. 1.

   Define a recurrence relation in your own words.

   Hint

   Think about how previous values influence the current term.

2. 2.

   What is an example of a linear homogeneous recurrence relation?

   Hint

   Look for relations where coefficients are multiplied with preceding terms.

3. 3.

   What is a recurrence equation?

   • An equation defining terms of a series
   • A type of polynomial
   • An algebraic expression

   Hint

   Think of how sequences are constructed in mathematics.

4. 4.

   True or False: Characteristic roots can be the same.

   • True
   • False

   Hint

   Recall what we discussed about distinct and repeated roots.

5. 5.

   Given the recurrence relation An - 4An-1 + 3An-2 = 0, determine its characteristic equation and roots.

   Hint

   Set the equation to zero and factor it for roots.

6. 6.

   Derive a specific sequence from the general relation An = 5An-1 - 6An-2 given initial conditions A0 = 2 and A1 = 3.

   Hint

   Substitute n=0 and n=1 to solve for c1 and c2.