The formula for the partial sum of a geometric sequence is given by:
[tex]S_n=\frac{a(r^n-1)}{r-1}[/tex]
From the problem, we identify:
[tex]\begin{gathered} n=7 \\ a=3 \\ r=2 \end{gathered}[/tex]
Finally, using these values in the formula:
[tex]\begin{gathered} S_7=\frac{3(2^7-1)}{2-1}=\frac{3(128-1)}{1}=3\cdot127 \\ \\ \therefore S_7=381 \end{gathered}[/tex]
