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Math Help - The nth term that is killing me

  1. #1
    Salsa
    Guest

    Exclamation The nth term that is killing me

    So basically I've got this set of numbers and I've found the pattern but i can't figure out how to into a formula. It's kinda important because it's part of my coursework, which really needs to be posted in the next few days.

    So here be the numbers

    3,12,30,60,105,168,252
    1st set of differences:
    9,18,30,45,63,84
    2end set of differences:
    9,12,15,18,21,24
    3erd set of differences:
    3,3,3,3,3

    I think it's something to do with n^3 but I really can't figure it out.

    Help please?
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  2. #2
    Flow Master
    mr fantastic's Avatar
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    Quote Originally Posted by Salsa View Post
    So basically I've got this set of numbers and I've found the pattern but i can't figure out how to into a formula. It's kinda important because it's part of my coursework, which really needs to be posted in the next few days.

    So here be the numbers

    3,12,30,60,105,168,252
    1st set of differences:
    9,18,30,45,63,84
    2end set of differences:
    9,12,15,18,21,24
    3erd set of differences:
    3,3,3,3,3

    I think it's something to do with n^3 but I really can't figure it out.

    Help please?
    You can fit the numbers to a cubic model:

    t_n = \frac{n^3}{2} + \frac{3n^2}{2} + n.

    Of course higher degree models also work, so the simple fact is that there's no unique formula.

    (But no doubt the person who set this question will be expecting the above cubic formula).
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  3. #3
    Senior Member DivideBy0's Avatar
    Joined
    Mar 2007
    From
    Melbourne, Australia
    Posts
    432
    Quote Originally Posted by Salsa View Post
    So basically I've got this set of numbers and I've found the pattern but i can't figure out how to into a formula. It's kinda important because it's part of my coursework, which really needs to be posted in the next few days.

    So here be the numbers

    3,12,30,60,105,168,252
    1st set of differences:
    9,18,30,45,63,84
    2end set of differences:
    9,12,15,18,21,24
    3erd set of differences:
    3,3,3,3,3

    I think it's something to do with n^3 but I really can't figure it out.

    Help please?
    You know:

    t_n=an^3+bn^2+cn+d

    And:

    t_1 = 3

    t_2 = 12

    t_3 = 30

    t_4 = 60

    Can you now use simultaneous equations to find a, b, c, and d?
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