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Math Help - nth term of the sequence help

  1. #1
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    nth term of the sequence help

    Hey I need some help with this math problem.

    Find a formula for the nth term of the sequence
    1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, ...

    I can see the pattern, but I'm not sure how to go about finding a formula for this sequence. Hoping someone can guide me through this problem so I can understand it better thanks.
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  2. #2
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    Re: nth term of the sequence help

    The term in the interval (n(n-1)/2, n(n+1)/2]is n. The pattern generalizes as follows: The first term is 1, the next two terms is 2, etc... (as you already know). So, every number (k) repeats k times, and the successive terms increase by 1, after repetition, starting from 1. It means, the nth term has to do with how many numbers are below it, and since each number repeats itself "its value" number of times, this has to do with sum of first n numbers. Once you cross, sum of first n numbers terms, you get a new value for the term in the series.

    Salahuddin
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  3. #3
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    Re: nth term of the sequence help

    sorry, i already understand how the pattern works, what im looking for is someone to guide me through the problem to find a formula for this sequence, thanks for your help anyways
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    Re: nth term of the sequence help

    The term in the interval (n(n-1)/2, n(n+1)/2]is n. Doesnt that give a formula?

    Salahuddin
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  5. #5
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    Re: nth term of the sequence help

    Quote Originally Posted by gfbrd View Post
    Hey I need some help with this math problem.
    Find a formula for the nth term of the sequence
    1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, ...
    I can see the pattern, but I'm not sure how to go about finding a formula for this sequence. Hoping someone can guide me through this problem so I can understand it better thanks.
    This involves triangular numbers. The rule uses the floor function.
    s_n  = \left\lfloor {\frac{{1 + \sqrt {8n - 7} }}{2}} \right\rfloor .
    Thanks from gfbrd
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    Re: nth term of the sequence help

    Thanks guys for your help

    Edit: Plato do you think you can explain to me how you get that answer?
    Last edited by gfbrd; October 31st 2012 at 09:11 PM.
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    Re: nth term of the sequence help

    Quote Originally Posted by gfbrd View Post
    Thanks guys for your help
    Edit: Plato do you think you can explain to me how you get that answer?
    The triangular numbers \frac{n(n+1)}{2}+1,~~2,~4,~7,~11,~16,~\cdots are places in your sequence where the terms "change". That is, from the 10^{th}+1 term to the 15^{th} term the sequence terms are 5 and n=4 gives the fourth triangular number. The floor function gives an integer. From terms 11\text{ to }15 \left\lfloor {\frac{{1 + \sqrt {8n - 7} }}{2}} \right\rfloor=5 at term 16 it changes to 6 for the next six terms.
    Last edited by Plato; November 1st 2012 at 06:18 AM.
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  8. #8
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    Re: nth term of the sequence help

    oh alright thanks a lot plato
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