2022-II-37

由於它們為等比數列的項，可得

$\begin{array}{rcl}{\displaystyle \frac{a_2}{a_1}}& =& {\displaystyle \frac{a_3}{a_2}}\\ {\displaystyle \frac{1}{8p^2}}& =& {\displaystyle \frac{27p}{1}}\\ p^3& =& {\displaystyle \frac{1}{216}}\\ p& =& {\displaystyle \frac{1}{6}}\end{array}$

所以，公比

$\begin{array}{cl}=& {\displaystyle \frac{a_2}{a_1}}\\ =& {\displaystyle \frac{1}{8(\frac{1}{6}{)}^2}}\\ =& {\displaystyle \frac{9}{2}}\end{array}$

由此，可得

$\begin{array}{rcl}{a}_4& =& a_1{r}^3\\ a_4& =& 8{\left({\displaystyle \frac{1}{6}}\right)}^2\times {\left({\displaystyle \frac{9}{2}}\right)}^3\\ a_4& =& {\displaystyle \frac{81}{4}}\end{array}$