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Homework Help: Formula and Sequence

  1. Apr 10, 2010 #1
    I just wanted to know if anybody had a trick to find the formula for the general term of a sequence.

    I can find some without troubles. But other like 1,0,1,0,1,0... I don't know how to find them.

    Thank you!
  2. jcsd
  3. Apr 10, 2010 #2


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    Of course you know that technically, the next term could be anything and the first few terms of a sequence never determines a pattern. So these questions always involve a subjective judgement or guess what the author intends. In this case one suspects the described sequence is to consist of alternating 1's and 0's. It is more a matter of experience than anything to come up with a formula. This might suggest sin(n pi/2) for n = 1,2,..., which gives:

    1 0 -1 0 1...

    Not quite it. Put absolute values on it: |sin (n pi/2)|:

    1 0 1 0 ... works.

    Another thing you might think of is using (-1)n, which alternates the sign:

    -1 1 -1 1 -1 1...

    Try adding 1 to it: 1 + (-1)n: 0 2 0 2 0 2...

    Close. Divide it by 2: (1 + (-1)n)/2: 0 2 0 2 0 2 if you start with n = 1. So start with n = 0.

    Each problem presents its own challenges.
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