# sequence

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Related to Ordered sequence: Finite sequence

## sequence

sequence, in mathematics, ordered set of mathematical quantities called terms. A sequence is said to be known if a formula can be given for any particular term using the preceding terms or using its position in the sequence. For example, the sequence 1, 1, 2, 3, 5, 8, 13, … (the Fibonacci sequence) is formed by adding any two consecutive terms to obtain the next term. The sequence −1-2, 1, 7-2, 7, 23-2, 17, … is formed according to the formula (n2 − 2)/2 for the nth, or general, term. A sequence may be either finite, e.g., 1, 2, 3, … 50, a sequence of 50 terms, or infinite, e.g., 1, 2, 3, … , which has no final term and thus continues indefinitely. Special types of sequences are commonly called progressions. The terms of a sequence, when written as an indicated sum, form a series; e.g., the sum of the sequence 1, 2, 3, … 50 is the series 1 + 2 + 3 + … + 50.
The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

## Sequence

a fundamental concept of mathematics. A sequence is a set of elements of any nature that are ordered as are the natural numbers 1,2,…, n…. It can be written in the form x1, x2, …, xn, … or simply {xn}. The elements of which it is composed are called its terms. Different terms of a sequence may be identical.

A sequence may be regarded as a function whose argument can take on only positive integral values—that is, a function defined on the set of natural numbers. To define a sequence, we can either specify its nth term or make use of a recurrence formula, by which each term is defined as a function of preceding terms. Fibonacci numbers, for example, are defined through a recurrence formula. The sequences most often encountered are those of numbers or functions. For example,

(1) 1, 2, …, n, …

that is, xn = n

If the terms of a sequence of numbers differ by an arbitrarily small amount from the number a for sufficiently large n, the sequence is said to be convergent, and a is called its limit. The limit of a sequence of functions is defined in a similar manner. For example, sequences (2) and (4) are convergent, and their limits are 0 and the function 1/(1 + x2), respectively. Sequences that are not convergent are said to be divergent. Sequences (1) and (3) are examples of divergent sequences.

## sequence

[′sē·kwəns]
(computer science)
To put a set of symbols into an arbitrarily defined order; that is, to select A if A is greater than or equal to B, or to select B if A is less than B.
(engineering)
An orderly progression of items of information or of operations in accordance with some rule.
(geology)
A sequence of geologic events, processes, or rocks, arranged in chronological order.
A geographically discrete, major informal rock-stratigraphic unit of greater than group or supergroup rank. Also known as stratigraphic sequence.
A body of rock deposited during a complete cycle of sea-level change.
(mathematics)
A listing of mathematical entities x1, x2… which is indexed by the positive integers; more precisely, a function whose domain is an infinite subset of the positive integers. Also known as infinite sequence.
(meteorology)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

## sequence

1.
a. Cards a set of three or more consecutive cards, usually of the same suit
b. Bridge a set of two or more consecutive cards
2. Music an arrangement of notes or chords repeated several times at different pitches
3. Maths
a. an ordered set of numbers or other mathematical entities in one-to-one correspondence with the integers 1 to n
b. an ordered infinite set of mathematical entities in one-to-one correspondence with the natural numbers
4. a section of a film constituting a single continuous uninterrupted episode
5. Biochem the unique order of amino acids in the polypeptide chain of a protein or of nucleotides in the polynucleotide chain of DNA or RNA
6. RC Church another word for prose
Collins Discovery Encyclopedia, 1st edition © HarperCollins Publishers 2005
References in periodicals archive ?
In particular, the research presented here focuses on testing the generality of the Hogarth and Einhorn (1992) belief-updating model, which was developed to explain order effects - that is, how differently ordered sequences of the same information can result in different judgments.
d) If the set of remaining (n-k) jobs is empty, list the n-jobs ordered sequence, or schedule, and its total completion time, as final solution.
Working with embryologist Thomas Hunt Morgan in the legendary "fly room" at Columbia, Sturtevant arranged the ordered sequence of genes for eye color, wing shape, body size, and other characteristics based on their appearance in consecutive generations of Drosophila.
If this is done with enough copies of a genome, the resulting data enable sophisticated computer software to match overlapping fragments and ultimately reassemble a complete, correctly ordered sequence of DNA.
(In the neutral case of four or more nodes lying on a common circle, one or more Voronoi edges degenerates to a point.) Thus, given a Delaunay triangulation, the Voronoi region associated with a node is defined by the (cyclically) ordered sequence of circumcenters of the triangles containing the node.
For the generalized manufacturing task computer simulation, an "assembling" program is set up, which has to associate different database figures, expressing the symbols of the ordered sequences. The program converts the alphanumeric ordered sequence into a succession, joining geometric figures that comply with this ordered sequence.
A handful of scientists are picking apart infants' utterances and finding that not only is there an ordered sequence of vocal stages between birth and the first words, but in hearing-impaired babies a type of babbling thought to signal an emerging capacity for speech is delayed and distorted.
"Things" in their enduring self-presence or self-identity, accordingly, must be deconstructed so as to make clear that they are in fact "event-nexuses," ordered sequences of microscopic self-creative "events." F.

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