Answer:
[tex]-171,875[/tex]Explanation:
Here, we want to find the sum of the geometric series
Mathematically, we have the mathematical formula to calculate this as follows:
[tex]S_n\text{ = }\frac{a(1-r^n)}{1-r}[/tex]where:
a is the first term which is given as -11
n is the number of terms wich is 7
r is the common ratio which is -4
Substituting the values, we have it that:
[tex]\begin{gathered} S_n\text{ = }\frac{-11(1-(-4))\placeholder{⬚}^7}{1+4} \\ \\ S_n\text{ = }\frac{-11(5)\placeholder{⬚}^7}{5}\text{ = -11 }\times\text{ 5}^6\text{ = -171,875} \end{gathered}[/tex]