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Math Help - Sequences

  1. #1
    Member CalcGeek31's Avatar
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    Sequences

    Write an explicit expression for the n-th term of the sequence.


    2,5,10,17,26,37,50,65,82,101


    I know that it increases by two more than the last increase each time, ie a1-a0 = 3 and a2-a1=5 and a3-a2=7

    I would prefer instruction rather than just the simple answer please
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  2. #2
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    Go to ths site and type in your sequence.
    See what you get as an answer.
    The On-Line Encyclopedia of Integer Sequences
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  3. #3
    MHF Contributor
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    Quote Originally Posted by CalcGeek31 View Post
    Write an explicit expression for the n-th term of the sequence.


    2,5,10,17,26,37,50,65,82,101


    I know that it increases by two more than the last increase each time, ie a1-a0 = 3 and a2-a1=5 and a3-a2=7

    I would prefer instruction rather than just the simple answer please
    If the difference betwee two consecuative numbers is constant then the solution would look like a_n = c_1 n + c_0 for some constants c_0 and c_1 but because the difference of difference is 2, the the formula would look like a_n = c_2 n^2 + c_1 n + c_0

    Let's look for patterns

    a1 = 2
    a2 = 5 = 4 + 1
    a3 = 10 = 9 + 1
    a4 = 17 = 16 + 1
    a5 = 26 = 25 + 1
    a6 = 37 = 36 + 1

    see the pattern?
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