# sequence

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Related to sequence: Arithmetic 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 progressionsprogression,
in mathematics, sequence of quantities, called terms, in which the relationship between consecutive terms is the same. An arithmetic progression is a sequence in which each term is derived from the preceding one by adding a given number, d,
. The terms of a sequence, when written as an indicated sum, form a seriesseries,
in mathematics, indicated sum of a sequence of terms. A series may be finite or infinite. A finite series contains a definite number of terms whose sum can be found by various methods. An infinite series is a sum of infinitely many terms, e.g.
; 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 It might be outdated or ideologically biased.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 ?
The visualization of sequence information and sequence analysis information can help in forming an intuitive understanding of the genomic data and enable the efficient representation of the results.
While the structure of an n-bit LFSR can be easily deduced from 2n consecutive bit of its sequences, by applying the Berlekamp-Massey algorithm, up to O(2n) bits would be needed to determine the structure of a n-bit NLFSR generating a given sequence [12], thus denoting a stronger resistance to attacks aimed at breaking the sequence generation algorithm.
For these types of sequencing jobs, the sequencing cost would cost slightly more than \$3,000 per sequence, which is still a more than 10X (\$30,000+) improvement on the sequencing costs seen just five years ago.
In summary, T2-weighted sequences in body MRI are typically performed with a fast spin-echo sequence.
There are 5 possible positions for a P sequence embedded in a P sextuplet.
Our new system for rapid determination of viral RNA sequence (RDV) uses whole-genome amplification and direct sequencing techniques (Figure 1).
We develop a qualitative analysis of asynchronous forum of several e-learning courses identifying sequences or moves of teaching discourse.
Kashihara [2] asked: How many primes are there in the sequence. Ashbacher [3] explored this question and raised some more questions, which "were studied and answered by Henry Ibstedt [4].
Although much effort has focused on the gene-environment axis, there is a growing body of information that suggests that environmental influences may extend beyond the DNA sequences of our genes.
His first ad was a barf sequence, but Birdhouse must be feeling sick to their stomachs after losing this hot-shot to the F-troop.
In addition to germline sequencing, we used this strategy to sequence somatic mutations that occur during tumorigenesis.
In part 2, Coe and Church provide a clear explanation of their version of sequence stratigraphy, which incorporates the use of the Falling Stage System Tract (FSST) to record sedimentation between the onset and end of base level fall.

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