The adjective started out simply enough in the seventeenth century to refer to a person who was inclined to follow a leader; almost at once it took on the idea of slavishly or unreasoningly following the ideas of other people. It’s unusual but still around:
I could discern omens of nothing newer than the old fate of the sequacious: to be for ever at the mercy of the exploiting proclivities of the bold and buccaneering in their bullying and greed.
Prelude to Waking, by Miles Franklin, 1950
Other senses you may very occasionally come across are of a thing that follows another with logic and unwavering direction of thought or form, or of musical notes that succeed each other with unvarying regularity (Coleridge described “long sequacious notes” in a poem). I’d guess this is the sense meant in this rare modern example:
When she closed her fingers around it, the shapes flared briefly once more, and she saw that they were indeed runes: inexplicable to her, but sequacious and acute.
Fatal Revenant, by Stephen R Donaldson, 2007.
To call writing non-sequacious is to say that it lacks logic, that it jumps about from one topic to another and that it’s replete with non-sequiturs. That word is appropriate, since both sequacious and sequitur are from the Latin verb sequi, to follow, from which we also get sequel and sequence. The immediate source of sequacious is sequax, following; sequitur is the third-person present tense of sequi, meaning “it follows”, though it so often doesn’t that we mainly use the negative.
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