2002 AMC 12B Problem 13

The sum of $n,$ $n+1,\ldots,$ $n+17$ is $18n+\dfrac{17\cdot18}{2}=9(2n+17).$ Since $9$ is a perfect square, $2n+17$ must be one too. The smallest positive integer $n$ making $2n+17$ a perfect square is $n=4,$ giving $2n+17=25$ and a sum of $9\cdot25=225.$ Thus, the correct answer is B.