Answer
$S_{7}=\dfrac{127}{21}$
Work Step by Step
Using $S_{n}=\dfrac{a_1(1-r^n)}{1-4}$, the sum of the first $
7
$ terms of the sequence $
3,\dfrac{3}{2},\dfrac{3}{4},...
$ is
\begin{array}{l}
S_{7}=\dfrac{3\left(1-\left( \dfrac{1}{2} \right)^7\right)}{1-\dfrac{1}{2}}\\\\
S_{7}=\dfrac{3\left( \dfrac{127}{126} \right)}{\dfrac{1}{2}}\\\\
S_{7}=\dfrac{\dfrac{127}{42}}{\dfrac{1}{2}}\\\\
S_{7}=\dfrac{127}{21}
.\end{array}