正项递增等比数列 \( \left\{{a}_{n}\right\}\) ，若 \( {a}_{2}+{a}_{4}=30\) ， \( {a}_{1}{a}_{5}=81\) ，则 \( \frac{{a}_{2}}{{a}_{4}}=\) ___．

\( \left\{\begin{array}{c}{a}_{2}{a}_{4}=81\\\ {a}_{2}+{a}_{4}=30\end{array}\right.\) ，解得 \( \left\{\begin{array}{c}{a}_{2}=3\\\ {a}_{4}=27\end{array}\right.\) ，或 \( \left\{\begin{array}{c}{a}_{4}=3\\\ {a}_{2}=27\end{array}\right.\) 

因为 \( \left\{{a}_{n}\right\}\) 是正项递增的等比数列，所以 \( \left\{\begin{array}{c}{a}_{2}=3\\\ {a}_{4}=27\end{array}\right.\) ，即 \( \frac{{a}_{2}}{{a}_{4}}=\frac{1}{9}\) .

进入考试题库