Sequences and series..... My text book says that a progression is another name for a series, but the dictionary says it is another name for a sequence - which is it?
progression: 3. A continuous series; a sequence. -The American Heritage® Dictionary of the English Language I think it is both.
A sequence is an ordered set of terms, {[itex]t_i[/itex]} A series is a sum of terms, [itex]\sum t_i[/itex] Mathworld defines a 'progression' as synonymous with 'sequence'. PS : An English dictionary does not necessarily know the mathematical difference between a sequence and a series.
A series is a special kind of sequence. if your sequence is x1, x2, x3, x4, x5... then the series it produces is x1, x1+x2, x1+x2+x3, x1+x2+x3+x4, ... which we can re-label as y1, y2, y3, y4, ... and this is a new sequence. so if a progression is a series, then it is automatically a type of sequence. Also, there are arithmetic progressions, geometric progressions, and others. My idea of progression is any sequence, including the special sequence called a series. Aaron