数列 $\left\{a_{n}\right\}$ 中, $a_{1}=1$, 以后各项由公式 $a_{1} \cdot a_{2} \cdot a_{3} \cdot \ldots \cdot a_{n}=n^{2}$ 给出, 则 $a_{3}+a_{5}$ 等于 ( )
答案: C

解析: $\because a_{1} \cdot a_{2} \cdot a_{3} \cdots a_{n}=n^{2}$

$\therefore a_{1} \cdot a_{2} \cdot a_{3}=32=9$,

$a_{1} \cdot a_{2}=2^{2}=4$,

$\therefore a_{3}=\frac{9}{4}$.

$\therefore a_{1} \cdot a_{2} \cdot a_{3} a_{4}=4^{2}=16$,

$a_{1} \cdot a_{2} \cdot a_{3} \cdot a_{4} \cdot a_{5}=5^{2}=25$,

$\therefore a_{5}=\frac{25}{16}$,

$\therefore a_{3}+a_{5}=\frac{9}{4}+\frac{25}{16}=\frac{61}{16}$.

故选 C.