Etymology
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sequence (n.)

late 14c., in church music, a composition said or sung after the Alleluia and before the Gospel, from Old French sequence "answering verses" (13c.) and directly from Medieval Latin sequentia "a following, a succession," from Latin sequentem (nominative sequens), present participle of sequi "to follow" (from PIE root *sekw- (1) "to follow").

In Church use, a partial loan-translation of Greek akolouthia, from akolouthos "following." By 1570s in the general sense of "a series of things following in a certain order, a succession," also in cards, "a run of three or more consecutive numbers of the same suit." By 1580s as "order of succession." In biochemistry in reference to nucleic acids, by 1959.

sequence (v.)

"arrange in a sequence," 1954, in computing, from sequence (n.). In biochemistry by 1970. Related: Sequenced; sequencing.

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Definitions of sequence
1
sequence (n.)
serial arrangement in which things follow in logical order or a recurrent pattern;
he invented a technique to determine the sequence of base pairs in DNA
the sequence of names was alphabetical
sequence (n.)
a following of one thing after another in time;
the doctor saw a sequence of patients
Synonyms: chronological sequence / succession / successiveness / chronological succession
sequence (n.)
film consisting of a succession of related shots that develop a given subject in a movie;
Synonyms: episode
sequence (n.)
the action of following in order;
he played the trumps in sequence
Synonyms: succession
sequence (n.)
several repetitions of a melodic phrase in different keys;
2
sequence (v.)
arrange in a sequence;
sequence (v.)
determine the order of constituents in;
They sequenced the human genome
From wordnet.princeton.edu