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Math Help - arithematic progressions.

  1. #1
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    Question arithematic progressions.

    find 'd' if sum of first 'm' term is 'xm^2+ym'?
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  2. #2
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    Hello, anjana!

    What a strange problem . . .


    Find d if sum of first m terms is: . xm^2 + ym

    The sum of the first m terms is: . S_m\;=\;\frac{m}{2}\left[2a + d(m-1)\right]
    . . where a is the first term and d is the common difference.

    So we have: . \frac{m}{2}\left[2a + d(m-1)\right] \:=\:xm^2 + ym
    . . which equals: . \left(\frac{d^2}{2}\right)m^2 + \left(a - \frac{d}{2}\right)m \;= \;xm^2 + ym


    Two polynomials are equal if their corresponding coefficients are equal.

    . . Hence, we have: . \frac{d^2}{2} \,=\,x\quad\Rightarrow\quad\boxed{ d \,=\,\sqrt{2x}}

    Without additional information, that's the best we can do.

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