16.7.2. RHS Expression Explanation

Try these first

1. 1.

   Define a recurrence relation in your own words.

   Hint

   Focus on how sequences can be interconnected.

2. 2.

   What are initial conditions?

   Hint

   Think about why certain values are needed at the beginning.

3. 3.

   What is a recurrence relation?

   • A polynomial function
   • An equation defining a sequence based on previous terms
   • A random number generator

   Hint

   Think about how sequences are 'recursive' in nature.

4. 4.

   True or False: Initial conditions are unnecessary for calculating terms in a recurrence relation.

   • True
   • False

   Hint

   Consider the foundation of a building; without starting points, you can't build up.

5. 5.

   Given a recurrence relation f(n) = f(n-1) + f(n-2) and f(1) = 1, f(2) = 1, find f(5).

   Hint

   Break down to previous values step by step.

6. 6.

   How would you set up a recurrence for a scenario where you're counting valid sequences of a different form, say starting with 2 and increasing?

   Hint

   Define your new starting point and conditions.