sekʷ-eyo-
“to keep following, pursuing”second, sequel, consequence, execute
Iterative of *sekʷ- giving Latin sequī, English second, sequel, consequence, execute, persecute.
Discussion
The form *sekʷ-eyo- is an iterative-causative derivation from the root *sekʷ- "to follow," built with the *-eyo- suffix that in Proto-Indo-European regularly expressed repeated or intensified action — here, "to keep following, to pursue persistently." Pokorny (IEW 896–897) establishes the root with a wide array of reflexes across the family, and Rix (LIV² 524) confirms the base as *sekʷ- with a labiovelar that conditions distinctive developments in each branch.
Latin sequī "to follow" is the central reflex, and its derivatives pervade English through centuries of legal and ecclesiastical borrowing. Second originally meant "the one following the first," from Latin secundus, a gerundive formation. Sequel and sequence preserve the bare notion of one thing following another, while consequence introduces the idea that events follow from causes. The legal senses are especially striking: prosecute (to follow forward, to pursue a case), persecute (to follow through relentlessly), and execute (to follow out to completion, to carry through) all encode social acts of pursuit and enforcement through prefixed forms of sequī. Greek hépesthai "to follow" descends from the same root with the expected loss of the initial sibilant before the vowel.
The semantic thread running through all these descendants is remarkably stable: from the Proto-Indo-European speaker who followed a trail or a leader, to the Roman magistrate who prosecuted a case, to the modern English speaker who follows a sequence of arguments, the core image of one thing coming after another in purposeful motion has never been lost.