what is the sum of all odd integers between 10 and 28

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what is the sum of all odd integers between 10 and 28

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Cora 1 month 2021-08-13T15:23:26+00:00 1 Answer 0 views 0

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    2021-08-13T15:25:02+00:00

    \underline{\textsf{To find:}}

    \textsf{Sum of all odd integers between 10 and 28}

    \underline{\textsf{Solution:}}

    \textsf{Consider,}

    \textsf{Sum of all odd integers between 10 and 28}

    \mathsf{=11+13+15+.......+27}

    \textsf{This can be written as}

    \mathsf{=(1+3+........+9)+11+13+15+.......+27-(1+3+........+9)}

    \mathsf{=(1+3+..............+27)-(1+3+........+9)}

    \mathsf{=(\dfrac{m+1}{2})^2-(\dfrac{n+1}{2})^2}

    \mathsf{=(\dfrac{27+1}{2})^2-(\dfrac{9+1}{2})^2}

    \mathsf{=(14)^2-(5)^2}

    \mathsf{=196-25}

    \mathsf{=171}

    \underline{\textsf{Answer:}}

    \textsf{Sum of all odd integers between 10 and 28 is 171}

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