7. If the integer $k$ is added to $36,300,596$, respectively, the results are the squares of three consecutive terms in an arithmetic sequence, find the value of $k$.
7. Let $\left\{\begin{array}{l}36+k=(n-d)^{2} , \\ 300+k=n^{2} \\ 596+k=(n+d)^{2}\end{array}\right.$
(1)
From (3) - (1) we get $4 n d=560$,
$\therefore n d=140$.
From (2) $\times 2-(1)-$ (3) we get $2 d^{2}=32$,
$\therefore d= \pm 4$, then $n= \pm 35$.
From (2), $k=n^{2}-300=35^{2}-300=925$.