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Math Help - Make the Equation

  1. #1
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    Make the Equation

    okay, i cant reamber how to make the equation for this problem and i need help:

    okay it starts a 0, then the first number is 3000, second, 9000, third, 18000, 4th 30000 so on..

    so it increases by 3000 for each time it adds, but i cant reamber how to make the problem, that was like 2 years agao
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by Lammalord View Post
    okay, i cant reamber how to make the equation for this problem and i need help:

    okay it starts a 0, then the first number is 3000, second, 9000, third, 18000, 4th 30000 so on..

    so it increases by 3000 for each time it adds, but i cant reamber how to make the problem, that was like 2 years agao
    The n-th term is:

    s(n) = 3000*(n-1).

    alternativly you can write it as:

    s(1)=0,
    s(n+1) = s(n) + 3000.

    RonL
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  3. #3
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    Quote Originally Posted by Lammalord View Post
    okay, i cant reamber how to make the equation for this problem and i need help:
    okay it starts a 0, then the first number is 3000, second, 9000, third, 18000, 4th 30000 so on..
    so it increases by 3000 for each time it adds, but i cant reamber how to make the problem, that was like 2 years agao
    Hi,

    I rewrite your problem using a table:

    Code:
      n       a_n         factorized
      1       3000       = 1 * 3000
      2       9000       = 3 * 3000
      3      18000       = 6 * 3000
      4      30000       = 10 * 3000
      ...    ......         ......
    In general you need an equation : a_n = f * 3000, where f is a factor with respect to n.

    As you may have noticed the factor is exactly the sum of the n:
    Code:
      n     sum
      1       1
      2       1+2 = 3
      3       3+3 = 6
      4       6+4 = 10
      ...     ...
    The sum of the first n positive integers is calculated by: S = (1/2)n(n+1)

    So your equation becomes:

    a_n = (1/2)n(n+1)*3000

    EB
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  4. #4
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    thanks for the equation guys, ya its sort of sad it wasnt even math homework or anything.. ill know to come back here if i ever have a problem again
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  5. #5
    Grand Panjandrum
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    Quote Originally Posted by CaptainBlack View Post
    The n-th term is:

    s(n) = 3000*(n-1).

    alternativly you can write it as:

    s(1)=0,
    s(n+1) = s(n) + 3000.

    RonL
    What rubbish, next time read the question properly:

    the sequence is: 0, 3000, 9000, 18000, 30000, ...

    the n-th term is:

    s(n)=3000*n*(n-1)/2

    (differes from earboth's solution as his sequence starts with 3000, not with 0
    as mine does)

    RonL
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  6. #6
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    i was wondering about that, it didnt work, but it did remind me how to set up thouse type's of qustions..
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