Mathematicians define a sequence as a function which maps some subset of the positive integers onto some subset of the real numbers. In simplest terms, a sequence is an ordered list of elements. In this article, we will take these elements to be real numbers to simplify the discussion. A finite sequence, then, is a finite ordered list of real numbers: a₁,a₂,a₃,...,a_n. Thus 1,2,4,8,16,32 is a finite sequence, as is -1,0,1,-1,0,1, and 1,3,5,7,9,...,99. When a finite sequence has more terms than we care to write down, we use three dots (...) to designate the numbers we are not listing individually. The three sequences given above all have a clearly discernable pattern, but that is not a requirement for sequences in general. It does happen that most of the sequences that are important in mathematics do have some kind of pattern...