$10 \cdot 41$ If 5 numbers are inserted between 8 and 5832 to form a geometric series, then the fifth term is
(A) 648.
(B) 832.
(C) 1168.
(D) 1944.
(E) None of the above answers is correct.
(1st American High School Mathematics Examination, 1950)
[Solution] Let the first term of the geometric series be $a_{1}$, and the common ratio be $q$. From $a_{k}=a_{1} q^{k-1}(k=1,2, \cdots, 6,7)$ and the given conditions, we know $a_{1}=8, \quad a_{7}=8 q^{6}=5832$, which gives $\quad q^{6}=729$. Therefore, $q= \pm 3, \quad a_{5}=8 q^{4}=648$. Hence, the answer is $(A)$.