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Math Help - Find the partial sum

  1. #1
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    Find the partial sum

    find the partial sum

    100
    6n
    n=10


    ok this is what i did but i didnt get the same answer as the book can someone tell me what i did wrong please?

    100
    6n
    n=10

    60+66+72+78+...

    a1=60 d=66-60--> d=6

    c=a1-d --> c=60-6 --> c= 54

    an= dn+c --> an= 6n+54 --> a100=6(100)+54 --> a100= 654

    Sn= n/2(a1+an) --> Sn=100/2(60+654) -->
    Sn= 35700 which is the wrong answer......aarrrrrrrrrrrrrrrrhhhhh

    i looked in the back of the book and the correct answer is 30,030. what did i do wrong?
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  2. #2
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    Quote Originally Posted by flexus View Post
    find the partial sum

    100
    6n
    n=10


    ok this is what i did but i didnt get the same answer as the book can someone tell me what i did wrong please?

    100
    6n
    n=10

    60+66+72+78+...

    a1=60 d=66-60--> d=6

    c=a1-d --> c=60-6 --> c= 54

    an= dn+c --> an= 6n+54 --> a100=6(100)+54 --> a100= 654

    Sn= n/2(a1+an) --> Sn=100/2(60+654) -->
    Sn= 35700 which is the wrong answer......aarrrrrrrrrrrrrrrrhhhhh

    i looked in the back of the book and the correct answer is 30,030. what did i do wrong?
    Arithmetic series: a = 60, d = 6, number of terms = 91. Substitute into the usual formula.
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  3. #3
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    sum of natural numbers from 1 to n is n(n+1)/2

    so your sum

    = 6*{(sum from n=1 to n=100) - (sum from n=1 to n=9)}
    = 6{100*101/2 - 9*10/2}
    = 6{5050 - 45}
    = 6{5005}
    =30030
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  4. #4
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    Quote Originally Posted by mr fantastic View Post
    Arithmetic series: a = 60, d = 6, number of terms = 91. Substitute into the usual formula.
    how did you get 91 for number of terms?
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  5. #5
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    Quote Originally Posted by flexus View Post
    how did you get 91 for number of terms?
    n = 10 to n = 100. How many values of n is that ....?
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  6. #6
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    Quote Originally Posted by mr fantastic View Post
    n = 10 to n = 100. How many values of n is that ....?
    100 -10 = 90 right? how did you get the 1
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  7. #7
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    Quote Originally Posted by flexus View Post
    100 -10 = 90 right? how did you get the 1
    There are 90 numbers from 11 to 100 inclusive. Therefore from 10 to 100 there are 91. Maybe you ought to write them all out and count them all.
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