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Math Help - sequence question

  1. #1
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    sequence question

    Hey everyone, I have a simple question.

    How can I find a formula for the following sequences (like in the form ((n+1)n)/2 etc):

    0,0,1,1,2,4,7,13,24

    and

    2,1,3,4,7,11,19,30


    Thanks
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  2. #2
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    Red face

    Quote Originally Posted by Nguyen View Post
    How can I find a formula for the following sequences (like in the form ((n+1)n)/2 etc)...
    You can find formulae by trying different options, set-ups, and techniques. In other words, use intelligent guessing.

    Quote Originally Posted by Nguyen View Post
    0,0,1,1,2,4,7,13,24
    0 + 0 + 1 = 1
    0 + 1 + 1 = 2
    1 + 1 + 2 = 4
    1 + 2 + 4 = 7

    ...and so forth.
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  3. #3
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    Quote Originally Posted by stapel View Post
    You can find formulae by trying different options, set-ups, and techniques. In other words, use intelligent guessing.


    0 + 0 + 1 = 1
    0 + 1 + 1 = 2
    1 + 1 + 2 = 4
    1 + 2 + 4 = 7

    ...and so forth.
    Thanks stapel, I looked at that website and keep trying my second sequence with a_(n-1), a_(n-2), a_(n+1), a_(n+2), etc and other techniques on that site but can't seem to find the pattern. That 19 is a problem for me! I want to know what number comes after 30, but I just can't get it. Anyone have any thoughts?

    Thanks
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  4. #4
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    Quote Originally Posted by Nguyen View Post
    Thanks stapel, I looked at that website and keep trying my second sequence with a_(n-1), a_(n-2), a_(n+1), a_(n+2), etc and other techniques on that site but can't seem to find the pattern. That 19 is a problem for me! I want to know what number comes after 30, but I just can't get it. Anyone have any thoughts?
    Thanks
    The sequence you have: 2,1,3,4,7,11,19,30
    contains an obvious typo: the 19 should be 18, meaning the 30 should be 29
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  5. #5
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    Quote Originally Posted by Wilmer View Post
    The sequence you have: 2,1,3,4,7,11,19,30
    contains an obvious typo: the 19 should be 18, meaning the 30 should be 29
    I believe it is not a typo.
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  6. #6
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    Do you also believe that the start of 2,1,3 is correct, not 1,2,3 ?

    All I can say is "have fun"....
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  7. #7
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    Quote Originally Posted by Wilmer View Post
    Do you also believe that the start of 2,1,3 is correct, not 1,2,3 ?

    All I can say is "have fun"....
    Yes, this question has been in the lecture notes for a long time to my knowledge. I believe how it it stated is correct. I can't do it so that is why I am asking for some expert help. It might be a trick question or something. If others think that the sequence 2,1,3,4,7,11,19,30 has a typo in it and therefore finding the next term can't be done then o.k.
    Last edited by Nguyen; September 12th 2010 at 08:53 PM.
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  8. #8
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    Reason I mentionned the start of 2,1,3 may be really 1,2,3 is this sequence
    which seems to be the one you're after:
    3,4,7,11,19,30 - OEIS Search Results

    If you ask me, it's kind of something "silly".
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  9. #9
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    Quote Originally Posted by Wilmer View Post
    Reason I mentionned the start of 2,1,3 may be really 1,2,3 is this sequence
    which seems to be the one you're after:
    3,4,7,11,19,30 - OEIS Search Results

    If you ask me, it's kind of something "silly".
    I think these questions in general are rather silly since there are infinitely many formulae we could provide for any finite sequence.

    http://www.mathhelpforum.com/math-he...es-155069.html

    That said, sometimes pattern searching can be fun, and it's good to be able to recognize common sequences like 0, 1, 4, 9, 25, 36, ..
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