what is the sum of a 7-term geometric series if the first term is -11, the last term is -45056, and the common ratio is -4

Respuesta :

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]