HELP!! Using the geometric sequence 2,2/3,2/9,. ,2/243, find the approximate sum of the geometric series. Round your answer to the nearest whole number.

Answer choices:

4

3

1

6

Answers

Answer 1

we can always get the common ratio of a geometric sequence by simply dividing the current term by the previous term, in this case for the sake of simplicity let's divide 2/3 by 2, so  

[tex]\cfrac{2}{3}\div 2\implies \cfrac{2}{3}\div \cfrac{2}{1}\implies \cfrac{2}{3}\cdot \cfrac{1}{2}\implies \cfrac{1}{3}\impliedby \textit{common ratio}[/tex]

so the sequence more or less looks like   [tex]2~~,~~\cfrac{2}{3}~~,~~\cfrac{2}{9}~~,~~\cfrac{2}{81}~~,~~\cfrac{2}{243}[/tex]

so we'd want the sum of the first 5 terms

[tex]\qquad \qquad \textit{sum of a finite geometric sequence} \\\\ \displaystyle S_n=\sum\limits_{i=1}^{n}\ a_1\cdot r^{i-1}\implies S_n=a_1\left( \cfrac{1-r^n}{1-r} \right)\quad \begin{cases} n=\textit{last term's}\\ \qquad position\\ a_1=\textit{first term}\\ r=\textit{common ratio} \end{cases} \\\\\\ S_5=2\left( \cfrac{1~~ - ~~(\frac{1}{3})^5}{1~~ - ~~\frac{1}{3}} \right)\implies S_5=2\left( \cfrac{~~\frac{242}{243}~~}{\frac{2}{3}} \right)\implies S_5=\cfrac{242}{81}\implies S_5=2\frac{80}{81}[/tex]


Related Questions

Please help me with this please and thank you

Answers

Answer:

so i wrote the steps but not the answers, if you want i can write the answers too

Step-by-step explanation:

hello! so here all you have to do is substitute the given points of x to the equation. then you put two points on the graph. (two points on each graph) i can write the answers if you want, but please try first! if you cant ill help some more and show how to do it.

Nine wolves, eight female and one male, are to be released into the wild three at a time. If the male wolf is to be in the first released group and order does not matter, in how many ways can the first group of three wolves be formed? 28 ways 36 ways 56 ways 84 ways.

Answers

The first group of three wolves can be formed in 28 ways.

We have been given that Nine wolves, eight female and one male, are to be released into the wild three at a time.

What is the meaning of combination?

A combination is a combination of n things taken k at a time without repetition.

We need to choose 1 male wolf out of 1 wolf male. So  we can choose one wolf as

[tex]c(1,1)=\frac{1!}{1!(1-1)!} =\frac{1!}{1!}=1!=1[/tex]

We can choose 1 male wolf in only 1 way.

Since the female wolfs are identical that means order doesn't matter, so we will use combinations.

We can choose 2 female wolves out of 8 as

[tex]C(8,2)=\frac{8!}{2!(8-2)!} =\frac{8\times 7 \times 6!}{2\times 1\times 6!} =\frac{8\times 7}{2} =28[/tex]

Therefore, we can choose 2 female wolves out of 8 female wolves in 28 ways.

We have to find number of ways in which the first group of three wolves can be formed we will multiply the ways of choosing 1 male wolf and 2 female wolves.

Number of ways farming first group of three wolves

1(28)=28

Therefore, the first group of three wolves can be formed in 28 ways

To learn more about the combination visit:

https://brainly.com/question/25821700

help me pleaseeeeeeeeee ​

Answers

for 2 points A(xa;ya) and B(xb;yb)

the slope is (yb - ya) / (xb - xa)

here

the slope = 4 = (17-r) / (4-(-1))

(17-r) / 5 = 4

17 - r = 20

r = 17 - 20

r = - 3

point (-1 ; -3)

Kyle goes to the movies with his friends. Each person buys a ticket and two equally priced snacks at the snack bar. Let ticket price be represented by t and the price of the snacks be represented by s. Kyle says the total cost can be represented by the expression 5(t + 2s). Which explanation represents Kyle’s thinking about how to find the total price?

A.
Add the price for each item bought by each person.

B .
Add the total cost of the tickets with the total cost of the snacks for all the people that went to the movie.

C .
Multiply the ticket total by the snack total.

D .
Multiply the total spent on tickets plus snacks by the number of people who went to the movie.

Answers

Answer:

The correct answer is actually D

Step-by-step explanation:

i am 100% correct because i just answered this

See

one ticket means it's only 1t or t

Two equally packed snacks means

2×s2s

So if no of friends be 5

Then total is 5(t+2s)

Option D

A house on the market was valued at $418,000. After several years, the value increased by 9 percent. By how much did the house’s value increase in dollars? What is the current value of the house?

Answers

$455,620

First you would find 9% of the original price.
418,000x0.09=37,620
Then add that total to the original price.
418,000+37,620=455,620

Identify the population and the sample. Lena wants to open a new restaurant in a mall and needs to determine what kind of food to serve to attract the most customers. Out of 1200 mall visitors, 200 are asked their food preference.

Answers

The total mall visitors is the population parameter of the experiment

The sample of the experiment is 200, while the population is 1200

How to identify the sample and the experiment?

From the question, we have the following parameters:

Total mall visitors = 1200Visitors interviewed = 200

The total mall visitors is the population while the visitors that were asked of their food preference are the sample

Hence, the sample of the experiment is 200, while the population is 1200

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https://brainly.com/question/9910540

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Answers

Answer:

n=5     x=6

Step-by-step explanation:

2n+1 +n = 16

3n+1 =16

3n=15

n=5

    2x+x+x+1 =25

4x+1=24

4x=24

x=6

The radius of a circle is 2 inches. What is the length of a 180

Answers

Answer:

4pi or 12.6

Step-by-step explanation:

I hope this helps

How to find the area of composite figure steps

Answers

Answer: To find the area of a composite figure or other irregular-shaped figure, divide it into simple, nonoverlapping figures. Find the area of each simpler figure, and then add the areas together to find the total area of the composite figure.

Step-by-step explanation:

find the sum of the interior angle measures of a regular polygon with 22 sides

Answers

Answer:

Step-by-step explanation:

We can split this into 20 triangles, each with an angle sum of 180 degrees.

So 180(20) = 3600 degrees.

Write x=2 in slope intercept form

Answers

When x=a the slope is undefined . And when y is b the slope is zero

A triangle has two sides of length 14 and 19. What is the largest possible whole-number length for the third side?

Answers

its 33 I checked it mark the one above me brainiest

Solve these equation

4(3-x)=(1-2x)​

Answers

To attempt this algebraic equation we will be multiplying 4 to (3 - x) bracket so as to form the term on L.H.S.

[tex]:\implies\tt{4(3 - x) = (1 - 2x)}[/tex]

[tex]:\implies\tt{(12 - 4x) = (1 - 2x)}[/tex]

[tex]:\implies\tt{12 - 4x = 1 - 2x}[/tex]

Combining like terms, we get,

[tex]:\implies\tt{12 - 1 = - 2x + 4x}[/tex]

[tex]:\implies\tt{11 = 2x}[/tex]

[tex]:\implies\tt{2x = 11}[/tex]

[tex]:\implies\tt{x = \frac{11}{2} }[/tex]

[tex]:\implies\tt{x = 5.5}[/tex]

The value of x is 5.5

Hey there!

4(3 - x) = (1 - 2x)

4(3) + 4(-x) = 1 - 2x

12 - 4x = 1 - 2x

-4x + 12 = -2x + 1

ADD 2x to BOTH SIDES

-4x + 12 + 2x = -2x + 1 + 2x

SIMPLIFY IT!

-2x + 12 = 1

SUBTRACT 12 to BOTH SIDES

-2x + 12 - 12 = 1 - 12

SIMPLIFY IT!
-2x = -11

DIVIDE -2 to BOTH SIDES

-2x/-2 = -11/-2

SIMPLIFY IT!
x = 11/2


Therefore, your answer should be:

x = 11/2


Good luck on your assignment & enjoy your day!



~Amphitrite1040:)

Which expression is equivalent to this equation attached? Please help! I will make brainliest

Answers

Step-by-step explanation:

please mark me as brainlest

I need help please help me

Answers

Method 1 :

replace x and y by their value 1 and 3

3 = 4(1) - 1 = 4-1 = 3

2(1) + 3 = 2 + 3 = 5

correct

Method 2 :

y = 4x - 1

2x + y = 5

y = 4x - 1

y = -2x + 5

y - y = 4x - 1 - ( -2x + 5 )

0 = 4x - 1 + 2x - 5

6x - 6 = 0

6x = 6

x = 6/6 = 1

y = 4x - 1

y = 4(1) - 1

y = 3

correct

Answer:

Yes the points (1,3) is the solution for the systems of equations that are shown

Step-by-step explanation:

y = 4x - 1

plug in the numbers

3 = 4(1) - 1

3 = 4 - 1

3 = 3 so this is correct

2x + y = 5

plug in the numbers

2(1) + 3 = 5

2 + 3 = 5

5 = 5

so that means the points are also a solution for BOTH

In the drawing, what must be the coordinates of D to show ABCD is a square?

Answers

The coordinates must be (4, 7), bc if you look at the graph closely, all you need is one more coordinate at the top to make a square.

yo can i get a hand here just so i dont get it wrong

Answers

ALGEBRAIC EXPRESSIONS

[tex]__________________________[/tex]

B. 72 IS THE QUOTIENT OF THE EXPRESSION72 is an addend in the expression and not the quotient.

Find the radius when the area is 452.16 in^2

Answers

area = pi x r²

3,14 x r² = 452,16

r² = 144

r = 12

(25 POINTS!!!!) HELP

Answers

Answer:

Step-by-step explanation:

What is the measure of < L

Answers

Answer:

C.

Step-by-step explanation:

Because of the K And j = K and L.Those are equal of the length.

And also, I believed the angel of K is 130 degrees ...

I hope it can help you a lots...Thanks.

Answer:

C

Step-by-step explanation:

typical property of isoceles triangle

properties:

1.- Base angles are equal

2. has two sides equal

☆the two above are key to identifying an isoceles triangle

the one above satisfies no.2

brainliest please

One day, the weather report shows that boston is experiencing a temperature of -27 degrees, while london is experiencing a temperature of 37 degrees. which city is colder?

Answers

Answer:

Obviously Boston, since -27 is much less than 37

I kinda need help : /

Answers

Answer:

  24 square units

Step-by-step explanation:

There are a couple of ways you can figure the area of the frame:

subtract the inner area from the outer areamultiply the width of the frame by the length of its centerline

__

Subtract

The dimensions of the outer rectangle are twice the frame width plus the dimensions of the inner rectangle. That makes them 8 wide by 6 high. Then the difference of areas is ...

  A = (8)(6) -(6)(4) = 48 -24 = 24 . . . . square units frame area

__

Width by Length

The centerline of the frame is a rectangle with 1 unit greater length and width than the inner rectangle. It is 7 units by 5 units, so will have a perimeter of ...

  P = 2(L+W) = 2(7+5) = 24 . . . . units

Then the area of the frame is this length multiplied by the width of the frame:

  A = (24)(1) = 24 . . . . square units frame area

Joel has 24 sports trophies. Of the trophies 1/8 are soccer trophies. How many soccer does Joel have ?

Answers

Answer:

We are given that Joel has 24 sports trophies, of the 24 trophies there are 1/8 soccer trophies.


1/8 of 24 is 3.

24 divided by 8 = 3 soccer trophies

There are 3 soccer trophies all the rest of the trophies, which is 21 trophies, will be other sports. 21 trophies + 3 soccer trophies = 24 trophies in total



Step-by-step explanation:

Have a great rest of your day
#TheWizzer

Will give
BRAINLY AND FIVE STARS and A THANKS

Answers

Answer:

k = 12h

Step-by-step explanation:

Since each of the inputs of h can be mutiplied by 12 to get the output k, the equation is k = 12h
Hope this helps :)

Using the Fibonacci sequence of numbers a5,a6,a7,a8,a9,a10,a11,a12,a13,a14,a15. Find the 3rd ration. Do not forget to change to %. a 423.6% b 161.8% c 261.8% d 50%

Answers

Answer: I'm sorry is this a real question

Hi please help me out and add an explanation if u can!

Answers

Question 1: Find the perimeter of the baseDefinition of Perimeter: it is all the side lengths of the shape added up

 

 What do we know

              -the pentagon is a regular pentagon meaning all its side lengths

               are equal since all the sides have one tick mark which says all        

               the side lengths are equal

     2. Solve:

                   Perimeter: 6 + 6 + 6 + 6 + 6 = 30cm

Question 2: Find the height of the prismHeight of the prism

                ⇒ distance between the base pentagon and the top pentagon

                         ⇒ Height is 6 cm

Question 3: Find the Lateral AreaDefinition of Lateral Area: it is only the area of the non-base faces

     ⇒ the non-base faces are the squares on the side of the figure

       ⇒ there are 5 squares

          ⇒ Lateral Area = 5 * (Area of Square) = 5 * (6 * 6) = 180 square cm

Question 4: Find the area of the base

  The formula for the pentagon's area ⇒ [tex]\frac{5}{2}*s*a[/tex]

s --> length of the sides of the pentagon --> 6cma --> apothem length --> 4.1 cm

       *apothem is the distance from the center of the pentagon to any

         one of the sides

           Area = [tex]\frac{5}{2} *6*4.1 = 15 * 4.1 =[/tex] 61.5 square centimeters

Question 5: Find the surface areaDefinition of Surface Area: all the areas of different sides added up

        Surface Area = 2 * (Area of Base) + (Lateral Area)

                                = 2 *61.5 + 180 = 123 + 180 = 303 square centimeters

Hope that helps!

   

 

Jacob had a cube. When Jacob made a cross section parallel to the base, what shape did the cross section form? trapezoid square parallel triangle

Answers

Answer: Square

Step-by-step explanation:

A cross section cut parallel to a base will be the same shape as the base itself, and the base of a cube is a square. :)

Answer:

A square because it is not diagonal.

Step-by-step explanation:

What is the missing numerator?

A: 1
B: 2
C: 3
D: 4

Answers

Answer:

C. 3

is the answer :)

hopefully this helps

Answer:

D: 4

Step-by-step explanation:

1) Make the 1/4 into 5/20 by multiplying top and bottom by 5/5

x/5 - 5/20 = 11/20

2) Move the 5/20 to the other side

x/5 = 11/20 + 5/20

3) Add the 2 fractions on the right

x/5 = 16/20

4) Make the fraction on the right have a denominator of 5 by dividing top and bottom by 4/4

x/5 = 4/5

5) Multiply both sides by 5

x = 4

The missing numerator is 4.

¡Practicamos!

create 10 sentences answer the questions asked

use this vocabulary:
el menú

la cuenta

el camarero / la camarera

el azúcar

el tenedor

la sal

la pimienta

la servilleta

el cuchillo

la cuchara

el vaso

el plato

la taza

me faltan

le traigo

me trae

de nada

¿algo más?

delicioso

¡Qué rica!

pedir

Tengo calor

Tengo frío

el postre

otro

tengo sueño

ahora

¿Qué desean Uds?



During the party, you will help serve food. To practice, pretend that you have to answer the following questions from guests.

1. ¿Dónde están los platos?

2. Me faltan la sal y la pimienta. ¿Me trae a la mesa?

3. ¡Qué rico! ¿Necesito azúcar o ya estátext annotation indicator en el café?

4. ¿Uds tiene camareros o necesito servir comida para mis niños?

5. Describe el menú por favor.

6. ¿Tienen otros postres con el pastel?

7. Necesito pedir refrescos. ¿Qué tipo tienen Uds.?

8. ¿Dónde están las servilletas?

9. Tengo frío. ¿Tienen Uds. algunas mesas a fueratext annotation indicator, en el sol?

10. ¿Cuál es la comida mejor, que Ud. recomienda?

Answers

Answer:

All

Computing

Commerce

verb

past tense: wrote

1.

mark (letters, words, or other symbols) on a surface, typically paper, with a pen, pencil, or similar implement.

"he wrote his name on the paper"

Similar:

put in writing

write down

put down

put in black and white

commit to paper

jot down

note

note down

make a note of

set down

take down

mark down

record

register

log

list

make a list of

inscribe

sign

scribble

scrawl

pencil

2.

compose, write, and send (a letter) to someone.

"I wrote a letter to Alison"

Similar:

correspond

write a letter

communicate

Triangle ABC was transformed to create triangle DEF.

2 triangles are shown. Triangle A B C has point A at the top, B on the bottom right, and point C on the bottom left. Triangle D E F has point D at the top, E on the bottom right, and F on the bottom left. The triangles are identical.
Which statement is true regarding the side in the image that corresponds to Side length B A?

Side length B C corresponds to Side length B A because they are about the same length.
Side length E D corresponds to Side length B A because they are in the same position.
Side length E F corresponds to Side length B A because the transformation is isometric.
Side length F D corresponds to Side length B A because the length is not preserved.

Answers

Answer: Side length E D corresponds to Side length B A because they are in the same position.

Step-by-step explanation:

Answer: b

Step-by-step explanation:

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