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