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

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 , then you can use the following formula to compute it's sum (if it is finite):

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

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

, , and

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

26?

step-by-step explanation:

the answer is:

the answer is:

to solve the problem, we need to remember the quotient of power property, it's defined by the following relation:

if we have a quotienf of powers that have the same base, we need to keep the same base and subtract the exponent of the denominator power to the exponent of the numerator power.

so, we are given the expression:

then, calculating we have:

hence, the answer is:

have a nice day!