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Related to sequence: Arithmetic 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.



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.


(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.
An orderly progression of items of information or of operations in accordance with some rule.
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.
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.


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 classic literature ?
The question for us now to solve is the sequence of events leading from a rifled jewel-case at one end to the crop of a goose in Tottenham Court Road at the other.
Consider the long sequence of incidents which have all pointed to some sinister influence which is at work around us.
Let me give you, with as much detail as I can, the sequence of events which have led us to this catastrophe.
You can imagine, Watson, with what eagerness I listened to this extraordinary sequence of events, and endeavored to piece them together, and to devise some common thread upon which they might all hang.
A whole sequence of new thoughts, hopeless but mournfully pleasant, rose in his soul in connection with that tree.
But results which depend on human conscience and intelligence work slowly, and now at the end of 1829, most medical practice was still strutting or shambling along the old paths, and there was still scientific work to be done which might have seemed to be a direct sequence of Bichat's.
I exulted in the boundless freedom of the design; the open air of that immense scene, where adventure followed adventure with the natural sequence of life, and the days and the nights were not long enough for the events that thronged them, amidst the fields and woods, the streams and hills, the highways and byways, hostelries and hovels, prisons and palaces, which were the setting of that matchless history.
For generations the war has been the perfectly obvious and apparent sequence of European events.
To recall those letters led her, by natural sequence, to another effort of memory.
Filled with these reflections, I was for some time heedless of the sequence of my own experiences, but soon I thought, "How came I hither?
Yet although Wordsworth gives us broad deserts of prose in his poetry, he himself knew the joy of words in lovely sequence.
In ordinary physical causation, as it appears to common sense, we have approximate uniformities of sequence, such as "lightning is followed by thunder," "drunkenness is followed by headache," and so on.