What is the sum f the first five termns of a geometric series with a_1=20 and r=1/4?

1705/64

Step-by-step explanation:

A geometric series contains terms that are in the form where is the first term and is common ratio.

A common ratio is the number that is used to find the next term by multiplying previous term by .

Now we can use a formula and we would be using where n is the number of terms you are adding and is the first term and r is the common ratio.

Before we do that, I'm going to do this without that formula. Sum means we are just going to add these terms after finding them.

The first term is 20.

The second term is (1/4)(20)=5.

Third term is (1/4)(5)=5/4.

Fourth term is (1/4)(5/4)=5/16.

The fifth term is (1/4)(5/16)=5/64.

Now we add them (20)+(5)+(5/4)+(5/16)+(5/64)

Putting this into the calculator gives me: 1705/64.

Now let's do the formula way as well.

Again we have:

r=1/4

n=5 since we adding the first 5 terms:

Dividing by 3/4 is the same as multiply by 4/3.

Multiplying first fraction by 64/64:

{tex]S_5=\frac{5115}{192}[/tex]

Dividing to and bottom by 3:

.

answer is 67%

step-by-step explanation:

step-by-step explanation:

points a and b are equidistant from the desired line, so the line you find by using them will go through point r.

using points other than a and b will give the desired line only if they are equidistant from r. if they are randomly located, the perpendicular line you create will not necessarily go through point r, hence will not be a solution to the problem.