Calculus
# Sequences and Series

Suppose $\{a_n\}$ is a sequence defined by $a_1 = 1, a_2 = 1,$ and $a_n = a_{n-1} + a_{n -2}$ for each natural number $n > 2.$

What is $a_6$?

A *geometric progression* is a sequence in which $a_n = r \cdot a_{n-1}$ for each natural number $n > 1$, where $r$ is a real number called the *common ratio*.

If $a_n$ is a geometric progression with $a_1 = 5$ and $a_6 = 160$, what is $a_3$?