$10 \cdot 11$ Let $0<a<1$, if $x_{1}=a, \quad x_{2}=a^{x_{1}}, \quad x_{3}=a^{x_{2}}, \cdots$, $x_{n}=a^{x_{n-1}}, \cdots$ then the sequence $\left\{x_{n}\right\}$
(A) is increasing.
(B) is decreasing.
(C) odd terms are increasing, even terms are decreasing.
(D) even terms are increasing, odd terms are decreasing.
(China High School Mathematics League, 1985)
[Solution] Since $0a^{x}=$ $x_{3}$. This allows us to rule out $(A)$ and $(B)$.
Also, from $1>a^{a}=x_{2}$, we get $x_{1}=a^{1}<a^{x_{2}}=x_{3}$, thus ruling out $(D)$. Therefore, the correct choice is $(C)$.