So a sequence is a set (list) of numbers, generally one that follows some rule.
1, 2, 3, ... etc. or
2, 4, 6, ...
Of course, sequences don't have to be numeric and some kinds of brain teaser problems will show a sequence of pictorials and invite the problem-solver to figure out the rule that generated that sequence and to compute the next object in the sequence.
I just looked up the word sequence on Etymology Online Dictionary. It derives as "hymn sung after the Hallelujah and before the Gospel," from O.Fr. sequence "answering verses" (13c.), from M.L. sequentia "a following, a succession," from L. sequentem (nom. sequens), prp. of sequi "to follow".
In math they also talk about series - which is the summation of the elements of an infinite sequence. Series comes from "1610s, "a number or set of things of one kind arranged in a line," from L. series "row, chain, series," from serere "to join, link, bind together, put," from PIE base *ser- "to line up, join" according to the same source.
So sequence is a succession and a series is a joining together. The distinction makes sense in light of their root words. Maybe now I won't keep forgetting which word means what.
