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Math Help - Arithmetic Series

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    Arithmetic Series

    Consider the Arithmetic progression with first term 1, common difference 3 and last term 100. If A is any set of 19 distinct numbers from the arithmetic progression, show that there must always be two numbers whose sum is 104.

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    Grand Panjandrum
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    Quote Originally Posted by acc100jt View Post
    Consider the Arithmetic progression with first term 1, common difference 3 and last term 100. If A is any set of 19 distinct numbers from the arithmetic progression, show that there must always be two numbers whose sum is 104.

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    The series is a_n=2n-2,\ n=1, .. , 34. That the  n and $$ m th terms sum to  104 means:

    (3n-2)+(3m-2)=104

    or:

    n+m=36

    Now both of  n=17 and  m=19 are in any set of  19 consecutive integers between  1 and  34 inclusive, etc.. .

    CB
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    What happen if i pick 19 integers between 1 and 34 inclusive, but may not be consectutive, then n=17 and m=19 may not be in the set...hmm
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  4. #4
    Grand Panjandrum
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    Quote Originally Posted by acc100jt View Post
    What happen if i pick 19 integers between 1 and 34 inclusive, but may not be consectutive, then n=17 and m=19 may not be in the set...hmm
    Oppss.. misread the question, will get back to you on that

    CB
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