$10 \cdot 24$ The sum of the first $n$ terms, $2n$ terms, and $3n$ terms of an arithmetic sequence with the first term $a$ and common difference $d$ are denoted as $S_{1}, S_{2}, S_{3}$, respectively. Let $R=S_{3}-S_{2}-S_{1}$, then $R$ is related to
(A) $a$ and $d$.
(B) $d$ and $n$.
(C) $a$ and $n$.
(D) $a, d$ and $n$.
(E) None of $a, d, n$.
(11th American High School Mathematics Examination, 1960)
［Solution］ From the given conditions and the formula for the sum of the first $n$ terms of an arithmetic sequence, we have
$$
\begin{array}{l}
S_{1}=\frac{n}{2}[2 a+(n-1) d], \\
S_{2}=\frac{2 n}{2}[2 a+(2 n-1) d], \\
S_{3}=\frac{3 n}{2}[2 a+(3 n-1) d] .
\end{array}
$$

Then $R=S_{3}-S_{2}-S_{1}=2 n^{2} d$, hence the answer is $(B)$.