Origins
The English word "sequence" traces its origins to the Late Latin term "sequentia," meaning "that which follows," "a following," or "a succession." This Late Latin noun derives from the present participle "sequēns," itself formed from the Latin verb "sequī," which means "to follow," "to come after," or "to pursue." The Latin verb "sequī" is a direct descendant of the Proto-Indo-European root *sekʷ-, reconstructed with the general meaning "to follow." This root is a prolific source of vocabulary across many Indo-European languages, particularly within the Latin and Romance language families, and through them into English.
The Proto-Indo-European root *sekʷ- is not only the foundation of "sequī" but also underlies a broad semantic field related to following, pursuing, or coming after in sequence or order. In Latin, "sequī" functioned as a deponent verb, meaning it had passive forms but active meanings, and it gave rise to numerous derivatives that entered English either directly or through Romance intermediaries. Among these are "sequel," denoting something that follows another; "consequence," literally "what follows together with"; "prosecute," meaning to follow forward or carry on; "persecute," to follow relentlessly; and "execute," to follow out to completion. The adjective "obsequious," meaning servilely compliant or "following after," also stems from this root, as does "sect," originally referring to a group that follows a particular path or doctrine.
Further English words connected etymologically to *sekʷ- include "sue" and "suit," which entered English via Old French "suivre," itself derived from Latin "sequī." Similarly, "pursue" comes from the Old French "poursuivre," combining the Latin prefix "pro-" (forward) with "sequī." The ordinal "second," meaning "the one that follows the first," comes from Latin "secundus," which is related to the same root but formed with a different suffix and meaning "following" or "favorable." The Italian "segue," meaning a smooth transition or continuation, derives from "seguire," the Italian reflex of Latin "sequī." Latin phrases such as "non sequitur," meaning "it does not follow," and adjectives like "intrinsic" and "extrinsic," which incorporate the root in the sense of "following inward" or "following outward," further illustrate the semantic breadth of this root.
Scientific Usage
The word "sequence" entered English in the fourteenth century, retaining the core meaning of "that which follows" or "a succession." Its use expanded over time to encompass the idea of a particular order in which related events, movements, or things follow one another. This sense is especially prominent in mathematical and computational contexts, where a "sequence" denotes an ordered set of elements arranged precisely in the order they follow one another. This technical usage preserves the etymological essence of the term, emphasizing the importance of order and succession.
It is important to distinguish the inherited Latin root "sequī" and its derivatives from later borrowings or semantic shifts. The English "sequence" is a direct borrowing from Late Latin "sequentia," rather than an inherited Germanic cognate. While English has inherited many Indo-European roots through its Germanic lineage, "sequence" belongs to the substantial layer of vocabulary borrowed from Latin during the Middle English period, particularly in scholarly, legal, and scientific contexts.
"sequence" is a word rooted in the Latin verb "sequī," itself derived from the Proto-Indo-European root *sekʷ-, meaning "to follow." Its semantic field encompasses notions of following, pursuing, and ordering, which have been preserved and elaborated upon in English through various related words and phrases. The term's introduction into English in the fourteenth century reflects the broader influence of Latin on English vocabulary, especially in abstract and technical domains. The continuity of meaning from "that which follows" to the modern concept of an ordered series reflects the enduring legacy of this ancient root.