Respuesta :
Answer:
D.
Step-by-step explanation:
You could find the 8 terms and then add them up.
Let's do that.
Luckily we have the common ratio which is -5. Common ratio means it is telling us what we are multiplying over and over to get the next term.
The first term is -11.
The second term is -5(-11)=55.
The third term is -5(55)=-275.
The fourth term is -5(-275)=1375.
The fifth term is -5(1375)=-6875.
The sixth term is -5(-6875)=34375.
The seventh terms is -5(34375)=-171875.
The eighth term is -5(-171875)=859375.
We get add these now. (That is what sum means.)
-11+55+-275+1375+-6875+34375+-171875+859375
=716144 which is choice D.
Now there is also a formula.
If you have a geometric series, where each term of the series is in the form [tex]a_1 \cdot r^{n-1}[/tex], then you can use the following formula to compute it's sum (if it is finite):
[tex]a_1\cdot \frac{1-r^{n}}{1-r}}[/tex]
where [tex]a_1[/tex] is the first term and [tex]r[/tex] is the common ratio. n is the number of terms you are adding.
We have all of those. Let's plug them in:
[tex]a_1=-11[/tex], [tex]r=-5[/tex], and [tex]n=8[/tex]
[tex]-11 \cdot \frac{1-(-5)^{8}}{1-(-5)}[/tex]
[tex]-11\cdot \frac{1-(-5)^{8}}{6}[/tex]
[tex]-11 \cdot \frac{1-390625)}{6}[/tex]
[tex]-11 \cdot \frac{-390624}{6}[/tex]
[tex]-11 \cdot -65104[/tex]
[tex]716144[/tex]
Either way you go, you should get the same answer.
