# sequence

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## 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.

## 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)

## 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
References in periodicals archive ?
Analysis of the first and second internal transcribed spacer sequences of the ribosomal DNA in Biomphalaria tenagophila complex (Mollusca: Planorbidae).
Differentiation of phylogenetically related slowly growing mycobacteria based on 16S-23S rRNA gene internal transcribed spacer sequences. J Clin Microbiol.
Spacer sequences were assigned according to published data (5,6,8).
Multiple sequence alignment of the concatenated spacer sequences was performed by using ClustalW (www.ebi.ac.uk/clustalw).
In Oran and Laghouat, an Orientalis biotype sharing the same Yp8 and Yp9 spacer sequences was found, but limited multiple spacer typing of Oran strains hampered further comparisons beyond the biotype level (3).
burgdorferii sensu lato, whereas rRNA spacer sequences showed the highest scores for B.
Partial 16S rRNA, RNA polymerase B, and citrate synthase genes and 16S-23S internal transcribed spacer sequences indicated that human isolates were similar to Candidatus B.
Phylogenetic trees obtained by using alignment of the 9 concatenated spacer sequences and the neighbor-joining, maximum parsimony, and maximum likelihood methods showed similar organizations.
Fingerprinting methods targeting polymorphic spacer sequences in the direct repeat (DR) region, including spoligotyping, have been used in some of these regions and in Bombay (13-15).

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