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Math Help - Arithmetic Sequences

  1. #1
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    Unhappy Arithmetic Sequences

    This is a question I really don't get. I've tried all the things i can think of, and the only clue i have is: Arithmetic Sequences (this is a topic I'm horrible at).

    The problem is

    Find the sum of all positive integers not greater than 10000 that are divisible by either 3 or 11 but not by both of them.'
    Can you please help me soon????
    Tkx
    Mikhael
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  2. #2
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    It's all the numbers divisible by 3 or 11 but NOT divisible by 33. Does that help?
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  3. #3
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    So...

    S3333, a = 3, d = 3

    S909, a = 11, d = 11

    Add those two answers together then subtract...

    S303, a = 33, d = 33
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  4. #4
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    Hello, Mikhael!

    We need the formula for the sum of an arithemtic series.

    The sum of the first n terms is: . S_n \:=\:\frac{n}{2}\bigg[2a + (n-1)d\bigg]

    . . where: a = first term, d = common difference.


    Find the sum of all positive integers not greater than 10000
    that are divisible by either 3 or 11 but not by both of them.

    Sum of multiples of 3: . S_3 \;=\; 3 + 6 + 9 + \hdots + 9999
    This is an arithmetic series with: . a = 3,\;\; d = 3,\;\; n = 3333
    Its sum is: . S_3 \:=\:\frac{3333}{2}\bigg[2(3) + 3332(2)\bigg] \:=\:16,668,333

    Sum of multiples of 11: . S_{11} \;=\;11 + 22 + 33 + \hdots + 9999
    This is an arithmetic series with: . a = 11,\;\;d=11\;\;n = 909
    Its sum is: . S_{11} \;=\;\frac{909}{2}\bigg[2(11) + 908(11)\bigg] \;=\;4,549,545

    Sum of multiples of 33: . S_{33} \;=\;33 + 66 + 99 + \hdots + 9999
    This is an arithmetic series with: . a = 33,\;\;d = 33,\;<br />
\;n = 303
    Its sum is: . S_{33} \;=\;\frac{909}{2}\bigg[2(33) + 302(33\bigg] \;=\;1,519,848


    The desired sum is: . S_3 + S_{11} - 2(S_{33}) \;=\;\boxed{18,178,182}

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  5. #5
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    Shouldn't that be 303/2 for the 3rd one?

    And why do you subtract twice the sum of the multiples of 33?
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