sequence

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Related to sequences: Geometric sequences

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,
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. 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.
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; 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 ?
Primers were provided in the WGA kit, but no information regarding their sequences was obtained.
the routes proposed for the sequences of interaction correspond to a particular way of structuring the discourse, categorized as direct teaching in the system of categories
Moreover, the people displayed distinctive rearrangements at five spots along the DNA sequence.
One of these approaches has focused on testing the nonsynonymous (potentially functional) variations in coding sequences (Botstein and Risch 2003; Collins et al.
As our technology is the first that was intentionally designed to sequence whole genomes, we are confident that having this license from a technology leader such as Pyrosequencing AB will ensure our first- mover advantage," added Dr.
The FBI Laboratory has established guidelines for the interpretation of differences and similarities between sequences.
This article looks at induction furnace charging sequence case histories from John Deere Foundry, Waterloo, Iowa, and Auburn Foundry (Plant 2), Inc.
Gene-IT, a leader in sequence search for research and IP, today announced that the company has hired Oliver Bayliss as Director of European Sales, to assist overseas sales efforts for its flagship GenomeQuest[TM] sequence search software suite.
We observed a 93-bp in-frame deletion within the glpD gene sequences obtained from ancient dental pulp specimens.
After two years of intensive efforts by an international consortium of researchers, the Brown Norway rat (Rattus norvegicus) joins the human and the mouse as the third mammalian genomic sequence to be completed.
The resulting sequences were aligned, and a similarity index based on the translation of the 984-bp gene fragment was calculated.
The specific goal is to reduce sequencing costs by at least four orders of magnitude--$1000 serves as a useful target cost for a mammalian-sized genome because the availability of complete genomic sequences at that cost would revolutionize biological research and medicine.