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sequence

The Columbia Encyclopedia, Sixth Edition | 2008 | The Columbia Encyclopedia, Sixth Edition. Copyright 2008 Columbia University Press. (Hide copyright information) Copyright

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 n th, 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 progressions . The terms of a sequence, when written as an indicated sum, form a series ; e.g., the sum of the sequence 1, 2, 3, … 50 is the series 1 + 2 + 3 + … + 50.

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"sequence." The Columbia Encyclopedia, Sixth Edition. 2008. Encyclopedia.com. 10 Jul. 2009 <http://www.encyclopedia.com>.

"sequence." The Columbia Encyclopedia, Sixth Edition. 2008. Encyclopedia.com. (July 10, 2009). http://www.encyclopedia.com/doc/1E1-sequence.html

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sequencer

The Concise Oxford Dictionary of Music | 1996 | | © The Concise Oxford Dictionary of Music 1996, originally published by Oxford University Press 1996. (Hide copyright information) Copyright

sequencer. Elec. device enabling a succession of several sounds (together with modifications in each) to be pre-set.

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MICHAEL KENNEDY and JOYCE BOURNE. "sequencer." The Concise Oxford Dictionary of Music. 1996. Encyclopedia.com. 10 Jul. 2009 <http://www.encyclopedia.com>.

MICHAEL KENNEDY and JOYCE BOURNE. "sequencer." The Concise Oxford Dictionary of Music. 1996. Encyclopedia.com. (July 10, 2009). http://www.encyclopedia.com/doc/1O76-sequencer.html

MICHAEL KENNEDY and JOYCE BOURNE. "sequencer." The Concise Oxford Dictionary of Music. 1996. Retrieved July 10, 2009 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O76-sequencer.html

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Sequence

The Concise Oxford Dictionary of World Religions | 1997 | | © The Concise Oxford Dictionary of World Religions 1997, originally published by Oxford University Press 1997. (Hide copyright information) Copyright

Sequence. A hymn, usually in couplets, sung in the mass on certain days after the epistle. In medieval times a large number of sequences (c.150 melodies and 400 texts, with at least 5,000 having been written) were in regular use, but in the missal only five are now printed.

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JOHN BOWKER. "Sequence." The Concise Oxford Dictionary of World Religions. 1997. Encyclopedia.com. 10 Jul. 2009 <http://www.encyclopedia.com>.

JOHN BOWKER. "Sequence." The Concise Oxford Dictionary of World Religions. 1997. Encyclopedia.com. (July 10, 2009). http://www.encyclopedia.com/doc/1O101-Sequence.html

JOHN BOWKER. "Sequence." The Concise Oxford Dictionary of World Religions. 1997. Retrieved July 10, 2009 from Encyclopedia.com: http://www.encyclopedia.com/doc/1O101-Sequence.html

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Free newspaper and magazine articles

Free Article Smarandache Pascal derived sequences.
Magazine article from: Smarandache Notions Journal; 1/1/2001
Free Article Depascalisation of Smarandache Pascal derived sequences and backward extended Fibonacci sequence.
Magazine article from: Smarandache Notions Journal; 1/1/2001
Free Article On a Smarandache partial perfect additive sequence.
Magazine article from: Smarandache Notions Journal; 1/1/2001

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Smarandache Pascal derived sequences.
Magazine article from: Smarandache Notions Journal; 1/1/2001; ; 700+ words ; Given a sequence say [S.sub.b]. We call it the base sequence. We define a Smarandache Pascal derived sequence [S.sub.d] as follows: [T.sub.n+1] = [n.summation over (k=0)][sup.r][C.sub.k] x [t.sub.k+1], where [t.sub.k] is the kth term of the base... Read more
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Magazine article from: Smarandache Notions Journal; 1/1/2001; ; 648 words ; Given a sequence [S.sub.b] (called the base sequence). [b.sub.1], [b.sub.2], [b.sub.3], [b.sub.4],... Then the Smarandache Pascal derived Sequence [S.sub.d] [d.sub.1], [d.sub.2], [d.sub.3], [d.sub.4... Read more
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Magazine article from: Smarandache Notions Journal; 1/1/2001; ; 700+ words ; Abstract: The sequence defined through [a.sub.2k+1]=[a.sub...studied in detail. It is proved that the sequence is neither convergent nor periodic...recently been posed. It is shown that the sequence has an amusing oscillating behavior... Read more
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Magazine article from: Smarandache Notions Journal; 1/1/2002; ; 700+ words ; ...present the results of investigation of Smarandache Concatenate Sequence formed from the sequence of Happy Numbers and report some primes and other results found from the sequence Key words: Happy numbers, Consecutive happy numbers, H-sequence... Read more
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Magazine article from: Tamsui Oxford Journal of Mathematical Sciences; 12/1/2007; ; 700+ words ; 1. Introduction A complex sequence, whose kth term is [x.sub.k] is denoted by {[x.sub.k]} or simply. Let [PHI] be the set of all finite sequences. A sequence x ={[x.sub.k]} is said to be analytic if [MATHEMATICAL EXPRESSION... Read more
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Magazine article from: Smarandache Notions Journal; 1/1/2001; ; 700+ words ; ...of any set of consecutive terms of a sequence = the product of the first and the last...Smarodache Friendly Pair with respect to the sequence. {1} SMARANDACHE FRIENDLY NATURAL NUMBER PAIRS: e.g. Consider the natural number sequence 1,2,3,4,5,6,7, ... then the Smarandache... Read more
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Magazine article from: Scientia Magna; 9/1/2006; ; 700+ words ; ...investigation of first 100100 terms of Smarandache Deconstructive Sequence and report soiree new primes and other results found from the sequence. Keywords The Smarandache deconstructive sequence. initial digits, trailing digits. Introduction The Smarandache... Read more

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