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Math Help - Formula from a sequence

  1. #1
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    Formula from a sequence

    I am trying to derive a formula for this sequence:

    3, 4, 6, 8, 12, ...

    Need Help!!
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by jyoung View Post
    I am trying to derive a formula for this sequence:

    3, 4, 6, 8, 12, ...

    Need Help!!
    one method:

    define the sequence as a function of n, where n \ge 1 is an integer.

    so you have 5 points. (1,3), (2,4), (3,6), (4,8), and (5,12). now we want to find a curve that passes through all those points. let the curve be given by:

    f(n) = an^4 + bn^3 + cn^2 + dn + e

    we have:

    f(1) = a + b + c + d + e = 3 ..............(1)
    f(2) = 16a + 8b + 4c + 2d + e = 4 ..............(2)
    f(3) = 81a + 27b + 9c + 3d + e = 6 .............(3)
    f(4) = 256a + 64b + 16c + 4b + e = 8.........(4)
    f(5) = 625a + 125b + 25c + 5d + e = 12 ..........(5)

    you have 5 equations, 5 unknowns. solve simultaneously
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