[tex]\small\boxed{\begin{array}{cc} \hline\sf \normalsize {Math \: \: \: Question}\\ \hline\end{array}}[/tex]
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The [tex]\rm\blue{answer}[/tex] is [tex] \frac{19171}{640} \\ [/tex]
[tex]\large\bold{Solution:}[/tex]
=[tex] \frac{a \:( 1 - r { }^{n} )}{1 - r} \\ [/tex]
=[tex] \frac{ \frac{2}{5}(1 - \frac{3}{2}) {}^{9} }{1 - \frac{3}{2} } \\ [/tex]
=[tex] \frac{ \frac{2}{5}(1 - \frac{19683}{512} )}{1 - \frac{3}{2} } \\ [/tex]
=[tex] \frac{ \frac{2}{5}( - \frac{19171}{512}) }{ - \frac{1}{2} } \\ [/tex]
=[tex] \frac{ \frac{19171}{1280} }{ - \frac{1}{2} } \\ [/tex]
=[tex] \frac{ - 19171}{1280} \times \frac{ - 2}{1} \\ [/tex]
=[tex] \frac{19171}{640} \\ [/tex]
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[tex]\begin{gathered}{\begin{gathered} \ \\ \huge \boxed{ \ddot \smile} \end{gathered}}\end{gathered}[/tex]
[tex]\large\color{red}\underline{\bold{{✧Smartbabble✧}}}[/tex]
