Sequence

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late Middle English (in sequence (sense 4 of the noun)): from late Latin sequentia, from Latin sequent- ‘following’, from the verb sequi ‘follow’.

wiktionary

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From Middle English sequence, [1] borrowed from French sequence(“a sequence of cards, answering verses”), from Late Latin sequentia(“a following”), from Latin sequens(“following”), from sequi(“to follow”); see sequent.

etymonline

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sequence (n.)

late 14c., "hymn sung after the Hallelujah and before the Gospel," from Old French sequence "answering verses" (13c.), 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." General sense of "succession," also "a sequence at cards," appeared 1570s.

sequence (v.)

"arrange in a sequence," 1954, from sequence (n.). Related: Sequenced; sequencing.