Sequences and series .

  1. 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?
  2. jcsd
  3. kreil

    kreil 641
    Gold Member

    3. A continuous series; a sequence.
    -The American Heritage® Dictionary of the English Language

    I think it is both.
  4. Gokul43201

    Gokul43201 11,044
    Staff Emeritus
    Science Advisor
    Gold Member

    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.
    Last edited: Nov 7, 2004
  5. 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.
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