imc

Suppose that the first number of the arithmetic sequence is $a$. We will try to compute the value of $S_n$. First, note that the sum of an arithmetic sequence is equal to the number of terms multiplied by the median of the sequence. The median of this sequence is equal to $a+n-1$. Thus, the value of $S_n$ is $n(a+n-1)=n^2+n(a-1)$. Then, $$\frac{S_{3n}}{S_n}=\frac{9n^2+3n(a-1)}{n^2+n(a-1)}=9-\frac{6n(a-1)}{n^2+n(a-1)}.$$ Of course, for this value to be constant, $6n(a-1)$ must be $0$ for all values of $n$, and thus $a=1$. Finally, we have $S_{20}=20^2=\boxed{400}$.