sequence

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Related to Sequence types: 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 It might be outdated or ideologically biased.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 ?
* Genetic linkage and sequence types of Salmonella typhimurium strains isolated from clinical samples were identified based on a typing method (MLST).
spa type MSSA # (%) MRSA # (%) PVL tetM t002 12 (70.6%) 5 (29.4%) 4 (MSSA) t084 7 (778%) 2 (22.2%) 1 (MSSA) 1 (MRSA) t11469 3 (75.0%) 1 (25.0%) 1 (MSSA) spa type Sequence type (ST) t002 ST 5, ST 15, ST 121 t084 ST 15 t11469 ST5
Complete nucleotide sequences of two [bla.sub.KPC-2]-bearing IncN Plasmids isolated from sequence type 442 Klebsiella pneumoniae clinical strains four years apart.
Another goal was to characterize Campylobacter population structure among these animals by multilocus sequence type (MLST) genotyping of the isolates.
ITS1 sequence variabilities correlate with 18S rDNA sequence types in the genus Acanthamoeba (Protozoa: Amoebozoa).
Predominance of Cronobacter sakazakii sequence type 4 in neonatal infections.
pneumoniae CC1 CC2 ST ST ST ST ST ST Other Year 3 17 19 2 7 14 ST Subtotal Total 2002 2 2 29 2003 3 2 5 24 2004 4 1 5 22 2005 3 1 4 20 2006 15 5 2 22 54 2007 12 7 19 42 2008 15 2 1 18 33 2009 12 1 13 23 2010 8 4 1 13 23 2011 13 2 3 1 19 26 2012 16 3 2 21 32 2013 1 1 5 2015 25 25 33 2016 12 3 1 2 18 51 Total 138 5 21 2 3 9 7 185 417 % 74.6 2.7 11.4 1.1 1.6 4.9 3.8 100 * CC, clonal complex; ST, sequence type. Figure 1.
Sequence type 1 group B Streptococcus, an emerging cause of invasive disease in adults, evolves by small genetic changes.
These serotype 2 strains belonged to clonal complex 1 and had the same molecular characterization (sequence type [ST] 1; cps2/ mrp+/ef+/sly+), with the exception of 1 human isolate that was ST3 (a single-locus variant of ST1) (Table 1).
suis sequence type ST1 European reference strain (GenBank accession no.
Temporal changes in BEXSERO[R] antigen sequence type associated with genetic lineages of Neisseria meningitidis over a 15-year period in Western Australia.
Multilocus sequence typing (MLST) permits differentiation of GBS strains into >700 sequence types (STs), which are grouped into a few clonal complexes (CCs) (5).

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