Sequence

An ordered, infinite list of numbers $a_1,a_2,a_3,\ldots$ — really just a function of the index $n$ .

A sequence $\{a_n\}$ is an ordered list of numbers $a_1,a_2,a_3,\ldots$ , indexed by the positive integers — formally, a function $a:\mathbb{N}\to\mathbb{R}$ with $a(n)$ written $a_n$ . A sequence can be given EXPLICITLY, by a formula for $a_n$ directly in terms of $n$ , or RECURSIVELY, by defining each term from the one(s) before it.

Examples

Explicit: $a_n=\dfrac{1}{n}$ gives $1,\ \frac12,\ \frac13,\ \frac14,\ldots$
Recursive: $a_1=1$ , $a_{n+1}=2a_n$ gives $1,2,4,8,16,\ldots$