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Need help is hard

  1. Jun 28, 2007 #1
    okay i think this goes in the right section, but is hard, what is the equation to predict the next numbers?

    when 1=2, 2=4, what is the equation, to predict the next numbers


    x---y
    1---2
    2---4
    3---8
    4---12
    5---18
    6---24
    7---32
    8---40
    9---50
    10---60
    11---72
    12---84
    13---98
    14---112
    15---128
    16---144
    17---162
    18---180
    19---200
    20---220


    and same for this one too
    x---y
    1---21
    2---47
    3---84
    4---131
    5---189
    6---257
    7---336
    8---425
    9---525
    10---635
    11---756
    12---887
    13---1029
    14---1181
    15---1344
    16---1517
    17---1701
    18---1895
    19---2100
    20---2315
     
    Last edited: Jun 29, 2007
  2. jcsd
  3. Jun 29, 2007 #2

    matt grime

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    Science Advisor
    Homework Helper

    Please don't use an equals sign when you don't mean an equality. 1 is not equal to 2, nor 2 to 4.

    The first is 'straight-foward', though you probably want an answer in some unreasonably nice form. Just look at the differences of consecutive terms: 2,4,4,6,6,8,8,10,10, etc. This means: if n=2k, or 2k+1 for some integer k, than the n'th term is.....
     
  4. Jun 29, 2007 #3

    HallsofIvy

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    Staff Emeritus
    Science Advisor

    You understand, I hope, that there are an infinite number of equations, f(n), that will give precisely those numbers up to n= 20 and then give different numbers for n= 21?

    For s sequence of n given numbers, there exist a unique n-1 degree polynomial which gives that sequence. That means there must exist 19 degree polynomials giving your two sequences. On way to find them is to Write out the general 19 degree polynomial, substitute the given values for x and y and solve the resulting 20 equations. Perhaps simpler is the Lagrange polynomial:

    For each (xi,yi) pair for the product
    [tex] y_i \frac{(x- x_1)(x-x_2)\cdot\cdot\cdot(x-x_n)}{(x_i-x_1)(x_i-x_2)/cdot/cdot/cdot(x_i-x_n)}[/tex]
    where the prolducts in the numerator and denominator include all x values except xi

    Then add them all together.
     
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