Question

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

Answer 1

`-171,875`

Step-by-step explanation:

Here, we want to find the sum of the geometric series

Mathematically, we have the mathematical formula to calculate this as follows:

`S_n\text{ = }(a(1-r^n))/(1-r)`

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:

`\begin{gathered} S_n\text{ = }\frac{-11(1-(-4))\placeholder{⬚}^7}{1+4} \\ \\ S_n\text{ = }\frac{-11(5)\placeholder{⬚}^7}{5}\text{ = -11 }*\text{ 5}^6\text{ = -171,875} \end{gathered}`