sequence: an ordered list of numbers

arithmetic sequence: difference between consecutive terms is constant
       ex: 2,4,6,8,...
       ***An=A1+(n-1)d

geometric sequence: difference between consecutive terms is determined by a common ratio
       ex: 3,9,27,81,... (ratio=3)
       ***Tn=T1(r^(n-1))

recursive sequence: a sequence in which a general term is defined as a function of one or more of the preceding terms. A sequence is typically defined recursively by giving the first term, and the formula for any term An+1 after the first term.

Here's an example of the sigma sum notation.

series: a sequence in which the terms are summed, not just listed.

convergent series: a series whose limit as n approaches infinity equals a real number

divergent series: a series whose limit as n approaches infinity doesn't equal a number, but instead positive or                                negative infinity