#### Answer

$\dfrac {3}{20}$

#### Work Step by Step

$r=\dfrac {\dfrac {-2}{27}}{\dfrac {1}{9}}=\dfrac {\dfrac {1}{9}}{\dfrac {-1}{6}}=\dfrac {-\dfrac {1}{6}}{\dfrac {1}{4}}=-\dfrac {2}{3}\Rightarrow S_{\infty }=\dfrac {a_{1}}{1-r}=\dfrac {\dfrac {1}{4}}{1-\left( -\dfrac {2}{3}\right) }=\dfrac {3}{20}$