$10 \cdot 20$ If $x \neq y$ and the sequences $x, a_{1}, a_{2}, y$ and $x, b_{1}, b_{2}, b_{3}, y$ are each arithmetic sequences, then $\frac{a_{2}-a_{1}}{b_{2}-b_{1}}$ equals
(A) $\frac{2}{3}$.
(B) $\frac{3}{4}$.
(C) 1 .
(D) $\frac{4}{3}$.
(E) $\frac{3}{2}$.
(29th American High School Mathematics Examination, 1978)
[Solution] If $a_{1}, d, a_{n}$ are the first term, common difference, and general term of an arithmetic sequence, respectively, then
$$
\begin{array}{l}
d=\frac{a_{n}-a_{1}}{n-1} . \\
\therefore \quad \frac{a_{2}-a_{1}}{b_{2}-b_{1}}=\frac{\frac{y-x}{3}}{\frac{y-x}{4}}=\frac{4}{3} \text {. } \\
\end{array}
$$

Therefore, the answer is $(D)$.