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Relevant wiki: Geometric Progression Sum

The common ratio is $r=\dfrac{-1}{\dfrac{2}{3}}=\dfrac{\dfrac{3}{2}}{-1}=\dfrac{-3}{2}$ .

The sum of the terms of a geometric progression is given by $s=\dfrac{a_1-a_1r^n}{1-r}$ where $a_1$ is the first term, $r$ is the common ratio, and $n$ is the number of terms. Substituting, we have

$s=\dfrac{\dfrac{2}{3}-\dfrac{2}{3}\left(\dfrac{-3}{2}\right)^7}{1+\dfrac{3}{2}}=\boxed{\dfrac{463}{96}}$