Sequence Definition

Sequence

A list of elements in order: $1^{\text{st}}\text{ element},2^{\text{nd}}\text{ element}\dots$ and so on.

• may be finite: may stop after $n$ steps
• may be infinite: may go on forever
• may be unique or may be repeated

Example

$1,0,0,1,0,1,0,0,1,1,1$

$3,8,13,18,23,\dots$

$1,4,9,16,25,\dots$

Notation

• We use the notation $a_n$ to denote the image of the integer $n$. We call $a_n$ a term of the sequence.
• We use the notation $\{a_n\}$ to describe the sequence.
• Sequences are described by listing the terms of the sequence in order of increasing subscripts.

Example

• Consider the sequence $\{a_n\}$ where $a_n=\frac{1}{n}$
• The list of the terms of this sequence denoted by $a_1,a_2,a_3,a_4,\dots ,$ are: $1,\frac{1}{2},\frac{1}{3},\frac{1}{4},\dots$