10-19 The first four terms of an arithmetic sequence are $a, x, b, 2x$, then the ratio of $a$ to $b$ is 
(A) $\frac{1}{4}$.
(B) $\frac{1}{3}$.
(C) $\frac{1}{2}$.
(D) $\frac{2}{3}$.
(E) 2 .
(38th American High School Mathematics Examination, 1987)
[Solution] From the given, we have $x-a=b-x=2 x-b$, that is
$$
b=\frac{3 x}{2}, \quad \text{ and } \quad x=b-a .
$$
$\therefore \frac{b-a}{b}=\frac{x}{\frac{3 x}{2}}$, which means $1-\frac{a}{b}=\frac{2}{3}$, thus $\frac{a}{b}=\frac{1}{3}$. Therefore, the answer is $(B)$.