Question

What is the sum of an 8-term geometric series if the first term is -11, the last term is 859,375, and the common ratio is -5?

Answer 1

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 $a_1 \cdot r^{n-1}$, then you can use the following formula to compute it's sum (if it is finite):

$a_1\cdot \frac{1-r^{n}}{1-r}}$

where $a_1$ is the first term and $r$ is the common ratio. n is the number of terms you are adding.

We have all of those. Let's plug them in:

$a_1=-11$, $r=-5$, and $n=8$

$-11 \cdot \frac{1-(-5)^{8}}{1-(-5)}$

$-11\cdot \frac{1-(-5)^{8}}{6}$

$-11 \cdot \frac{1-390625)}{6}$

$-11 \cdot \frac{-390624}{6}$

$-11 \cdot -65104$

$716144$

Either way you go, you should get the same answer.