# 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 ?
One can always lift an infinite walk in the graph to an infinite sequence.
Hence, when constructing the inverse map to [PHI] we have to be careful in constructing an infinite sequence which is 312-avoiding.
Hence, the infinite sequence g decomposes into d sequences, each of which is monotone.
Then by [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] we denote the set of all infinite sequences of elements from X: Hence [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] We define the addition of two sequences by ([a.
iii) Hypothetical frequentism: the probability of an event A in a reference class B is what the limit of the relative frequency of A's among the B's would be hypothetically if the actual (finite) sequence were extended to an infinite sequence.
Informally, the difference between a task and a super-task is that a task consists of a finite sequence of actions, while a super-task consists of an infinite sequence of actions.
Therefore, we refine our definition of a task to be any finite or infinite sequence of actions, of which only a finite number of actions are not null actions.
It follows that W determines in an intuitively natural way the probabilistic properties of any n-fold random sample from the same data source S, for the set [Omega] of all denumerably infinite sequences of members of A can, by partitioning them in the manner above, equally represent all possible sequences of n outcomes generated by S, n = 1, 2, 3,.
The weak and strong laws are proved for a possibility space [Omega] consisting of either n-fold or infinite sequences of outcomes, which are classified as either 0 or 1 by a corresponding sequence [X.

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