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,
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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 ?
A recent study exploring cSNPs in human genes associated with high-density cholesterol levels revealed larger numbers of rare ns-cSNPs with predicted functional significance when individuals at the extremes of the phenotypes were sequenced and compared (Cohen et al.
Earlier this year, Celera researchers called in 40 fruit fly scientists to help the company analyze the data encoded in the 120 million bases of the Drosophila melanogaster genome--the largest genome yet sequenced (SN: 2/26/00, p.
We sequenced the hspA and glmM genes of all 107 colonies.
The investigators haven't sequenced every base on chromosome 22.
Initially a pioneer in the field of bacterial genomics (scientists there sequenced the first bacterial genomes in 1995), TIGR has more recently broadened its scope to include nonbacterial species, including the parasites that cause malaria and sleeping sickness.
The yeast genome is nearly seven times the size of the genome of Haemophilus influenzae, the first bacterium to be sequenced (SN: 6/10/95, p.
Crawley, UK), and sequenced with Big Dye Terminator Cycle Sequencing Ready Reaction (Applied Biosystems, Warrington, UK).
Although these sequences are specific to the rice and rice blast genomes, they will provide a model system for understanding host-pathogen interactions in other cereals and staple food crops," says Ralph Dean, director of the North Carolina State University Fungal Genomics Laboratory and leader of the group that sequenced the M.
In contrast to the HGP's method, in which the order of the BACs is known before they are each sequenced individually and then reassembled, the shotgun method involves cutting the DNA into small, random, overlapping pieces that are then sequenced and reassembled using a computer that compares all the pieces and matches the overlaps, thus assembling the whole genome.
The question is no longer whether the genome will be sequenced, but with what urgency--and what money.
PCR was performed from at least two separate reverse transcription reactions, and products from at least two PCR reactions were sequenced in each case to ensure accuracy and exclude amplification artifacts.
However, since our main goal was to compare the sequences of the Spanish isolates with those of isolates from the rest of the world, we designed a specific PCR to amplify the VP1 5' end gene, where a collection of isolates from Germany had been sequenced (22).

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