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consecutive (adj.)

"uninterrupted in course or succession," 1610s, from French consécutif (16c.), from Medieval Latin consecutivus, from consecut-, past-participle stem of Latin consequi "to follow after," from assimilated form of com "with, together" (see con-) + sequi "to follow" (from PIE root *sekw- (1) "to follow"). Related: Consecutively.

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Definitions of consecutive from WordNet
1
consecutive (adj.)
one after the other;
Synonyms: back-to-back
consecutive (adj.)
in regular succession without gaps;
consecutive (adj.)
successive (without a break);
Synonyms: straight
2
consecutive (adv.)
in a consecutive manner;
Synonyms: sequentially
From wordnet.princeton.edu