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?

A. -143,231
B. -36,047
C. 144,177
D. 716,144

Answer 1

D.

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 (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 (1-(-5)^(8))/(1-(-5))`

`-11\cdot (1-(-5)^(8))/(6)`

`-11 \cdot (1-390625))/(6)`

`-11 \cdot (-390624)/(6)`

`-11 \cdot -65104`

`716144`

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