Chapter Summary

Suppose the closed formula for a particular sequence is a degree 3 polynomial. What can you say about the closed formula for:

1. The sequence of partial sums.

2. The sequence of second differences.

Consider the sequence given recursively by $a_1 = 4$, $a_2 = 6$ and $a_n = a_{n-1} + a_{n-2}$.

1. Write out the first 6 terms of the sequence.

2. Could the closed formula for $a_n$ be a polynomial? Explain.

Your magic chocolate bunnies reproduce like rabbits: every large bunny produces 2 new mini bunnies each day, and each day every mini bunny born the previous day grows into a large bunny. Assume you start with 2 mini bunnies and no bunny ever dies (or gets eaten).

1. Write out the first few terms of the sequence.

2. Give a recursive definition of the sequence and explain why it is correct.

3. Find a closed fo…