## 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?

 PhysOrg.com science news on PhysOrg.com >> Heat-related deaths in Manhattan projected to rise>> Dire outlook despite global warming 'pause': study>> Sea level influenced tropical climate during the last ice age
 Recognitions: Gold Member progression: 3. A continuous series; a sequence. -The American Heritage® Dictionary of the English Language I think it is both.
 Recognitions: Gold Member Science Advisor Staff Emeritus A sequence is an ordered set of terms, {$t_i$} A series is a sum of terms, $\sum t_i$ 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.

## Sequences and 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