$10 \cdot 36$ A number plus $20, 50, 100$ forms a geometric sequence, then the common ratio is
(A) $\frac{5}{3}$.
(B) $\frac{4}{3}$.
(C) $\frac{3}{2}$.
(D) $\frac{1}{2}$.
(E) $\frac{1}{3}$.
(10th American High School Mathematics Examination, 1959)
[Solution] Let the number be $c$, and the common ratio of the geometric sequence be $r$. From the problem, we have $(20+c)(100+c)=(50+c)^{2}$, which gives $c=25$. $\therefore$ Thus, the answer is $(A)$.
$$
r=\frac{50+c}{20+c}=\frac{5}{3} \text {. }
$$