Sequences: A sequence is of the form
$a_1, a_2, a_3, a_4, ...$
where the $a_n$ are real numbers. Technically, a sequence is a function whose domain is the set of natural numbers, and whose range is a subset of the real
numbers. Sequences may be defined in various ways:
By listing, and appealing (via the three dots) to your intuition. Suppose the sequence is
$\frac{1}{2}, \frac{2}{5}, \frac{3}{10}, \frac{4}{17}, \frac{5}{26}, \frac{6}{37}, ...$
Then the $n$-th term is
$a_n = $
Explicitly. For example, suppose $a_n = n^n$. Then $a_1 = $, $a_2 = $ and $a_3 = $