find 'd' if sum of first 'm' term is 'xm^2+ym'?
Hello, anjana!
What a strange problem . . .
Find $\displaystyle d$ if sum of first $\displaystyle m$ terms is: .$\displaystyle xm^2 + ym$
The sum of the first $\displaystyle m$ terms is: .$\displaystyle S_m\;=\;\frac{m}{2}\left[2a + d(m-1)\right]$
. . where $\displaystyle a$ is the first term and $\displaystyle d$ is the common difference.
So we have: .$\displaystyle \frac{m}{2}\left[2a + d(m-1)\right] \:=\:xm^2 + ym$
. . which equals: .$\displaystyle \left(\frac{d^2}{2}\right)m^2 + \left(a - \frac{d}{2}\right)m \;= \;xm^2 + ym$
Two polynomials are equal if their corresponding coefficients are equal.
. . Hence, we have: .$\displaystyle \frac{d^2}{2} \,=\,x\quad\Rightarrow\quad\boxed{ d \,=\,\sqrt{2x}}$
Without additional information, that's the best we can do.