Definition

Definition

A sequence is a collection of terms such that each term is indexed by a natural number.

Sequences may be finite or infinite, and their terms may be numbers or functions. For example, the following is a sequence of Fibbonachi numbers,

\left(1,1,2,3,5,8,13,\dots\right).

We can denote each term by its placement, for example F_3 = 2, and F_7 = 13.

Notation

We use (a_n) to denote a sequence, and a_n without parenthesis to denote the n^{th}-term of the sequence.

We also use the notation (a_1,a_2,a_3,\dots) to denote a sequence. All terms are sequential and commas are used to seperate terms.

It is common to formalize sequences through functions, though our intuitive understanding will work just fine for the purposes of analysis.