We must compute the partial sum of a geometric series with:
[tex]\begin{gathered} a_1=4, \\ a_n=128, \\ r=2. \end{gathered}[/tex]
The formula for the partial sum is:
[tex]S_n=\frac{a_1-a_n\cdot r}{1-r}\text{.}[/tex]
Replacing the values of the problem in the formula above, we get:
[tex]S_n=\frac{4-128\cdot2}{1-2}=\frac{4-256}{-1}=\frac{-252}{-1}=252.[/tex]
Answer
[tex]S_n=252[/tex]
