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Secuence and series

  1. Sep 12, 2007 #1
    is this a sequence or a series?
    1,9,25,49,81,121

    it could be both
    9=1+8x1
    25=9+8x2
    49=25+8x3
    and so on

    1=1^2
    9=3^2
    25=5^2
    49=7^2
    and so on
     
  2. jcsd
  3. Sep 12, 2007 #2
    Answer: Both. Every series is a sequence (trivial) and every sequence is a series. For example:
    As a sequence a, b, c, ...
    As a series a, a + (b - a), a + (b - a) + (c - b), ...

    eom
     
  4. Sep 13, 2007 #3
    hey, first of all you have to proof that 1,9,25,49,81,121 is a sequence with a pattern of some sort, or is it to obvious?

    well at least then comment on my answer.
     
  5. Sep 13, 2007 #4
    You didn't ask if it was a sequence with a pattern, you just asked if it was a sequence. It is. And it has a pattern. In fact all sequences have a pattern. For instance:
    Sequence: [itex]a_1, a_2, a_3, ... [/itex]
    Pattern: Let f be any function such that [itex]f(1) = a_1, f(2) = a_2, f(3) = a_3, ...[/itex]. Then the sequence is equal to f(1), f(2), f(3), ... This is in fact what you did. The function you chose was [itex]f(x) = (2x -1)^2[/itex]. There are other distinct functions which also have the same values at the integers. In fact I don't really know if you chose f as I described, or one of these others.

    I did. Your answer was 'it could be both' and I said that it is both.
     
    Last edited: Sep 13, 2007
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