Limit of a Sequence
Big Idea: What happens to the terms of a sequence as we go further and further out? Does the sequence "settle down" toward a specific number? If so, that number is called the limit of the sequence.
1. What is a Sequence?
A sequence is an ordered list of numbers following a specific rule. We write a sequence as:
$a_1, a_2, a_3, a_4, \ldots, a_n, \ldots$
where $a_n$ represents the $n$-th term. For example, the sequence $\frac{1}{1}, \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \ldots$ has the rule $a_n = \frac{1}{n}$.