A sequence is defined as an ordered list of numbers.
- Sequences are ordered, meaning two sequences that contain the same values but in a different order are not equal.
- Sequences can be infinite if a rule is defined, i.e $\{1, 1, 1, 1, ...\}; a_i = 1$ 

# Behavior
- A sequence is considered **increasing** if $a_n$ is smaller than $a_{n+1}$ for all $n$.
- A sequence is considered **decreasing** if $a_n$ is greater than or equal to $a_{n+1}$ for all $n$.
- Sequences exist that do not fall into either category, i.e, $a_n = (-1)^n$

- If the terms of a sequence grow $\{a_n\}$ get arbitrarily close to a single number $L$ as $n$ grows larger, this is noted by writing:
$$\lim_{n\to\infty} a_n = L$$ OR
$$ a_n \to L \text{ as } n \to \infty $$

and say that $a_n$ *converges* to $L$. If no $L$ exists, we say $\{a_n\}$ *diverges*.

# Properties of Sequences
> The below properties assume two sequences are defined, $a_n \to L$ and $b_n \to M$
1. $a_n + b_n \to L + M$
2. $C*a_n \to CL$ 
3. $a_n b_n \to LM$
4.