Mathematics, 26.07.2019 21:10 orangeicecream

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

Answers: 1

Show answers

Answers

Answer from: Maria3737

1705/64

Step-by-step explanation:

A geometric series contains terms that are in the form $a_1\cdot(r)^{n-1}$ where a_1 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 $S_n=\frac{a_1(1-r^n)}{1-r}$ where n is the number of terms you are adding and a_1 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

a_1=20

n=5 since we adding the first 5 terms:

$S_5=\frac{20(1-(\frac{1}{4})^5}{1-\frac{1}{4}}$

$S_5=\frac{20(1-\frac{1}{1024}){\frac{3}{4}}$

$S_5=\frac{20-\frac{20}{1024}}{\frac{3}{4}}$

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

$S_5=(20-\frac{20}{1024})\frac{4}{3}$

$S_5=20 \cdot \frac{4}{3}-\frac{20}{1024}\cdot\frac{4}{3}$

$S_5=\frac{80}{3}-\frac{5}{256} \cdot \frac{4}{3}$

$S_5=\frac{80}{3}-\frac{20}{256 \cdot 3}$

$S_5=\frac{80}{3}-\frac{5}{64 \cdot 3}$

$S_5=\frac{80}{3}-\frac{5}{192}$

Multiplying first fraction by 64/64:

$S_5=\frac{80(64)}{3(64)}-\frac{5}{192}$

$S_5=\frac{5120}{192}-\frac{5}{192}$

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

Dividing to and bottom by 3:

$S_5=\frac{1705}{64}$ .

Answer from: Quest

x = 0.5 or x = 4.5

step-by-step explanation:

$|2x-5|=4\iff2x-5=4\ \vee\ 2x-5=-4\qquad\text{add 5 to both sides}\\\\2x=9\ \vee\ 2x=1\qquad\text{divide both sides by 2}\\\\x=4.5\ \vee\ x=0.5$

Answer from: Quest

the answer is 200

step-by-step explanation:

this is a problem about poisson probabilities. i don't know if you've

already studied poisson distributions, or if you have a place to look

to read more about the subject.

here's how you can see a poisson distribution coming. when there are

a lot of events that may happen at any time (or any place), and when

you're counting how many of them happen at a particular time (or a

particular place), and each event is independent of the others, then

the result is a poisson distribution. this is roughly true for the

chocolate chips; one chip being in a cookie has only a small effect on

the probability that another chip will be in the cookie.

once you know you have a poisson distribution, you know a lot. there

is only one parameter to a poisson distribution, so if you know the

mean, you know everything. the form of the distribution is

probability of n chips = {[e^(-x)]*(x^n)} / (n! )

Another question on Mathematics

Mathematics, 21.06.2019 18:30

Over the last 8 nights, elyse earned the following in tips: {105, 120, 84, 95, 100, 132, 140}. if she earns $140 a night for the next four nights, which measure of center would increase more, the mean or median?

Answers: 3

Answer

Mathematics, 21.06.2019 19:30

Jada has a meal in a restaurant she adds up the prices listed on the menu for everything they ordered and gets a subtotal of $42.00. after tax the total is 45.99. what percentage of the subtotal is the total?

Answers: 2

Answer

Mathematics, 21.06.2019 20:00

With finding limits of multi variable !

Answers: 1

Answer

Mathematics, 21.06.2019 21:00

You have 12 balloons to blow up for your birthday party. you blow up 1/3, and your friend blows up 5 of them. what fraction of the baloons still need blowing up