Sequence

lastmod 2018-08-17created 2014-10-317 edits

A sequence (sequence of numbers) is a listing of numbers. In particular,

it means numbers listed in order according to a fixed rule, such as 1,1,2,3,5,8,13,21···.

Each number belonging to it is called a ‘term’ of the sequence (also called an ‘element’ or ‘member’). Since the terms of a sequence are distinguished by their order, (1, 2, 3) and (1, 3, 2) are clearly different sequences, and unlike sets, one number can appear in two terms at once, as in (1, 1, 2). The number of terms is called the ‘length’ of the sequence. The length of a sequence may be finite or infinite. Also, a sequence may follow a fixed rule, as in (2, 4, 6, 8, …), or follow no rule at all, as in (3, 7, 6, 5, …). And some sequences, like the binary (1,1,0,1,0,0,1,0,1), have no mathematical rule but do have a rule related to information.

Properties of the sum of a sequence (sigma)

See also

• Series
• SIGMA

Favorite site

• Wikipedia (en) description of sequences
• Math 1: Various sequences - Properties of sigma ¹
• [Recommended] Basic properties of sigma ²

References