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Thread: sum of odd numbers in sequence

  1. #1
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    sum of odd numbers in sequence

    sum of odd numbers in sequence-potw-2-2.pngI remember doing a question like this before but I forgot what to do
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  2. #2
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    Re: sum of odd numbers in sequence

    $\displaystyle{\sum_{k=0}^{1008}}~(2k+1) = $

    $2\displaystyle{\sum_{k=0}^{1008}}~k+\displaystyle {\sum_{k=0}^{1008}}~1 = $

    $2 \dfrac{(1008)(1009)}{2} + 1009 = 1009(1008+1) = 1009^2 = 1018081$
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  3. #3
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    Re: sum of odd numbers in sequence

    $a_1 + (a_1+1) + (a_1+2) + \, ... \, + (a_1+2017) = 27243$

    $S_{2018} = 27243 = \dfrac{2018}{2}[a_1 + (a_1+2017)] \implies a_1 = -995$

    sum of odd terms ...

    $-995 + (-993) + \, ... \, + (-995+2016) = \dfrac{1009}{2}(-995 + 1021) = 13117$
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  4. #4
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    Re: sum of odd numbers in sequence

    these answers are conflicting
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  5. #5
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    Re: sum of odd numbers in sequence

    Quote Originally Posted by Ilikebugs View Post
    these answers are conflicting
    The method and answer in post #3 are the correct ones.
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