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Math Help - Urgent! Please Help find rule for function

  1. #1
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    Exclamation Urgent! Please Help find rule for function

    x: 1__2__3__4__5__6__7
    y: 1__3__6__10_15_21_28


    can anyway find the rule of this table?? please also explain if possible.

    PLEASE PLEASE REPLY BY THURSDAY

    THANKS SO MUCH
    p.s dont worri about the underlines. i onli did it to aline the numbers
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  2. #2
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    Quote Originally Posted by Fibonacci View Post
    x: 1__2__3__4__5__6__7
    y: 1__3__6__10_15_21_28


    can anyway find the rule of this table?? please also explain if possible.

    ...
    Hello,

    1. you easily can detect that
    Code:
     s_(n+1) = s_n + n
    This is called a recursive definition of the serie s.

    To calculate with this equation isn't very useful.

    2. I'll arange the numbers of the serie and calculate the differences:

    Code:
    1   3   6   10   15   21   28   36   ...
      2   3   4    5    6    7    8
        1   1   1     1    1     1
    You see that the serie is an arithmetic serie of order 2. Therefore the general equation is:
    s_n = a*nē + b*n + c

    Now plug in the values of s_1, s_2 and s_3:

    Code:
    1 = a + b +c
    3 = 4a + 2b + c
    6 = 9a + 3b + c
    Solve this system of simultaneous equations. I've got: a = 1/2, b = 1/2, c = 0

    Therefore your serie has the equation:

    s_n = 1/2*nē + 1/2*n

    To check, calculate s_7 = 1/2*49 + 1/2*7 = 56/2 = 28

    EB
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  3. #3
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    if you have the two sequences

    1 2 3 4 5 6 7 ---- x
    1 3 6 10 15 21 28 ---- y

    the value of y is the sum of all the x values until that point

    1,2,3,4,5,6,7 ----x
    1,(2+1),(3+2+1),(4+3+2+1),(5+4+3+2+1),(6+5+3+3+2+1 ) (7+6+5+4+3+2+1) ----y


    so at any index of x the corresponding value of y will be the sum of all the values of x upto and including that index.

    so if we want to know the value of y when x = 8. the value is (8+7+6+5+4+3+2+1) = 36

    I hope that makes sense.
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  4. #4
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    sorry eb did not mean to double post but i guess we were posting at the same time. i much prefer your explanation
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  5. #5
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    Quote Originally Posted by chogo View Post
    sorry eb did not mean to double post but i guess we were posting at the same time. i much prefer your explanation
    Hello, Chogo,

    you are welcome!

    I think the more different solutions a poster get the better he can understand to solve his problem.

    And as you certainly have noticed it is common use at this forum that everybody publishes his version of a solution.

    EB
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  6. #6
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    This is called the triangle sequence.

    The equation is,
    a_n=(n)(n-1)/2

    (Did you know that every positive integer is the sum of at most three triangular numbers! -Fermat).
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  7. #7
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    thats great PH did not know that. I just read these numbers can be found in the diagonal starting at row 3 on pascals triangle

    also fibbonaci this wikipedia page seems like a good page for you to formulate your answer from
    Triangular number - Wikipedia, the free encyclopedia
    Last edited by chogo; February 14th 2007 at 07:39 AM.
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  8. #8
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    Thanks guys but seriously u ppl r too smart. i dont understnad any of ur explanations. but i managed to find the answer to my question. its y=x(x+1)/2.
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