find the sum of the series 9+3+1+........+1/27​

Answers

Answer 1

Answer:

364/27

Step-by-step explanation:

9, 3, 1, ... is a geometric sequence with common ratio r = 1/3.

 

The nth term is a1rn-1.

 

If a1rn-1 = 1/27, then 9(1/3)n-1 = 1/27

 

                                32(3-1)n-1 = 3-3

 

                                3231-n = 3-3

 

                                    33-n = 3-3

 

                                      3-n = -3

 

                                         n = 6

 

The sum, Sn, of the first n terms of a geometric sequence is given by Sn = a1(1 - rn) / (1 - r).

 

So, 9 + 3 + 1 + ... + 1/27 = S6 = 9(1 - (1/3)6) / (1 - 1/3)

 

                                              = 9(1 - 1/729) / (2/3)

 

                                              = (27/2)(728/729) = 364/27


Related Questions

On their last history test, Eric scored five more than twice the points that his friend Josh did. If they scored 134 points altogether, find Eric’s score
plz i need help ASAP

Answers

Answer: Eric got a 91

Step-by-step explanation:

Make two equations:

We know Eric scored 5 points more than 2 times Josh’s score. E=Eric J=josh

Equation: E = 5 + 2(J)

E + J = 134

Solve for E:

J= 134 - E

Plug it into first equation: E= 5+ 2(134-E)

E= 5+(268-2E) add 2E from each side

E+ 2E = 268 + 5 reduce

3E = 273 divide by 3 to find Eric score

E= 91

You can plug it back in to find what josh received 134-91 = 43

To fact check if you multiple josh score of 43 by 2 you receive 86 which is indeed 5 points lower that 91 so it’s correct.

Are 3/4 and 16/20 equivalent? Why or why not is one fraction smaller/larger than the other? How do you know

Answers

Answer:

No they are not equivalent because 3/4 would be equivalent to 6/8, 9/12, 12/16/ 15/20. 16/20 would be the greatest fraction because in its simplest form it would be 4/5.


The 12th term of the sequence is 16 the term to term rule is subtract 3.
Work out the 5th term of the sequence. *​

Answers

Answer:

a₅ = 37

Step-by-step explanation:

The term to term rule ' subtract 3 ' is the common difference d of an arithmetic sequence with n th term

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

Given a₁₂ = 16, then

a₁ + 11d = 16 ← substitute d = - 3

a₁ + 11(- 3) = 16

a₁ - 33 = 16 ( add 33 to both sides )

a₁ = 49 , then

a₅ = 49 + (4 × - 3) = 49 - 12 = 37

ANALYZEPLANSOLVEJUSTIFYEVALUATE Pay close attention as you work through this process. You'll be asked to write a journal entry at the end. Bottled water comes in cases of 24 bottles. You need 150 bottles of water for a school event. How many cases of water do you need to buy? Enter a unit that best describes the number. CHECK Number Unit Description

Answers

Answer:

7

Step-by-step explanation:

If a case contains 24 bottles, and if I need to buy 150 bottles, I would need to buy 150 / 24 = 6.25

Because the store would not sell the quarter of a case, I would need to buy 7 cases of water.

By what expression can 3
x-1 be multiplied to yield the product 3x3+5x2+x-1?

Answers

Answer:

x^2 + 2x + 1

Step-by-step explanation:

Divide the original equation by 3x-1

An anthill has a volume of 8792 mm3 of dirt. Its radius is 20 mm. How far does an ant have to crawl to get from the base of the cone to the top of the hill? (This is the
slant height, s, of the cone.) Answer the questions to find out.

Answers

Answer:

The slope is 29 mm.

Step-by-step explanation:

What we know:

The radius of this cone is 20 mm, and the height is 21mm

s = √r^2 + h^2

s = √20^2 + 21^2

s = √400 + 441

s = √841

s = 29 mm

The slant height of the cone is required,

The ant would have to crawl [tex]29\ \text{mm}[/tex]

Volume of cone

V = Volume of cone = [tex]8792\ \text{mm}^3[/tex]

r = Radius of cone = 20 mm

h = Height

s = Slant height.

Volume of a cone is given by

[tex]V=\dfrac{1}{3}\pi r^2h\\\Rightarrow h=\dfrac{3V}{\pi r^2}\\\Rightarrow h=\dfrac{3\times 8792}{3.14\times 20^2}\\\Rightarrow h=21\ \text{mm}[/tex]

From Pythagoras theorem we have

[tex]s=\sqrt{r^2+h^2}\\\Rightarrow s=\sqrt{20^2+21^2}\\\Rightarrow s=29\ \text{mm}[/tex]

Learn more about slant height:

https://brainly.com/question/6613758

Can someone guide me step by step on how I hack my grades on a apple/hp laptop

Answers

Answer:

no sorry lol but just try harder

pls help this is due today

Answers

Answer:

50.137

Step-by-step explanation:

You can split the triangle into two triangles both with base 3 and height 12

The area of the two triangles is

[tex]2 * (1/2) * B * H\\B*H = 3* 12 = 36[/tex]

The area of a circle is [tex]\pi r^2[/tex]

so the area of the semi circle with r(adius) 3 is

[tex]\pi r^2/2\\9\pi/2[/tex]

[tex]9\pi/2 + 36 = 50.137[/tex]

Let $f(x) = 2x - 3$ and $g(x) = x + 1$. What is the value of $f(1 + g(2))$?

Answers

Answer:

The value of f(1 + g(2)) is 5

Step-by-step explanation:

Let us solve the question

∵ f(x) = 2x - 3

∵ g(x) = x + 1

We need to find the value of f(1 + g(2))

That means we will replace x in f(x) by 1 + g(2)

→ g(2) means substitute x in g by 2

∵ g(x) = x + 1

∵ x = 2

∴ g(2) = 2 + 1

g(2) = 3

∵ x of f = 1 + g(2)

∵ g(2) = 3

∴ x of f = 1 + 3

x of f = 4

→ To find f(1 + g(2)) substitute 1 + g(2) by 4

∵ f(x) = 2x - 3

∵ x = 4

∴ f(4) = 2(4) - 3

∴ f(4) = 8 - 3

f(4) = 5

f(1 + g(2)) = 5

Bags of cat food can be
purchased in the sizes shown.
Drag the bags to the boxes to
order them based on their price per ounce

Answers

Answer:

(72 oz.     $17.99)------------>Least expensive

(32 oz.     $7.32)------------>middle

(48 oz.     $9.60)------------>most expensive

Step-by-step explanation:

Once you understand how to do it, it's easy!

Just divide the ounces by the price to findout the cost

72 ÷ 17.99 = 4.00

32 ÷ 7.32  = 4.37

48 ÷ 9.60 = 5.00

4.00 < 4.37 < 5.00

Least, Middle, most

Good Job! Pls Brainliest!   ;)

what is the answer to

-6+n=6
How do you solve it

Answers

Answer:

n=12

Step-by-step explanation:

-6+n=6

n=6+6

n=12

You have to leave the n by its self so u have to do the opposite of the sign -6 =6 so add the 6 to the other side which gives you 12 so n=12

What is the difference between comprehensive and collision coverage in an auto policy​

Answers

Answer:

their both the same

Step-by-step explanation:

add and subtract divide multiply

Can I please get HELP? ( Picture included)

Answers

Answer:

no entiendo la version de esa mathematica

Step-by-step explanation:

Answer:

i think it is 26.

Step-by-step explanation:

180-134=46

180-160=20 so

ABC (46)- XYZ (20)=26.

I promise u your gonna have a bright future if u help me with this ! and I'll brainlist ​

Answers

a)
x 0 1 2 3 4
y 5 10 15. 20. 25

b) x 0 1 2 3. 4
y 1. 10. 37. 82. 145

11. A) x = 0

y = 2x + 5

=> y = 2 * 0 + 5

=> y = 0 + 5 = 5

=> y = 5 (First blank)

x = 1

y = 2x + 5

=> y = 2 * 1 + 5

=> y = 2 + 5 = 7

=> y = 7 (Second blank)

x = 2

y = 2x + 5

=> y = 2 * 2 + 5

=> y = 4 + 5

=> y = 9 (Third blank)

x = 3

y = 2x + 5

=> y = 2 * 3 + 5

=> y = 6 + 5

=> y = 11 (Fourth blank)

x = 4

=> y = 2x + 5

=> y = 2 * 4 + 5

=> y = 8 + 5

=> y = 13 (Fifth blank)

11. B)  x = 0

=> y =  

=> y = 3 * 0 * 0 + 1

=> y = 0 + 1

=> y = 1 (First blank)

x = 1

=> y =  

=> y = 3 * 1 * 1 + 1

=> y = 3 + 1

=> y = 4 (Second blank)

x = 2

=> y =  

=> y = 3 * 2 * 2 + 1

=> y = 12 + 1

=> y = 13 (Third blank)

x = 3

=> y =  

=> y = 3 * 3 * 3 + 1

=> y = 27 + 1

=> y = 28 (Fourth blank)

x = 4

=> y =  

=> y = 3 * 4 * 4 + 1

=> y = 48 + 1

=> y = 49 (Fifth blank)

For more info, here's a picture,

If my answer helped, kindly mark me as the Brainliest!!

Thank You!!

Which of the following forms a proportion?
5/9 = 14/18 3/5 = 21/35 6/12 = 18/34 1/8 = 2/24

Answers

Answer:

3/5 = 21/35

Step-by-step explanation:

if you reduce 21/35 it is 3/5 so it is the same thing

Jaime needs a new roof on her house. The cash cost is $7500. She decides to finance the project by paying 20% down , with the balance paid in 36 monthly payments of $189.40. (a) What finance charge will Jaime pay? (b) What is the APR to the nearest half percent ?

Answers

Answer:

(a) What finance charge will Jaime pay?

$818.4

(b) What is the APR to the nearest half percent ?

8.5%

Step-by-step explanation:

(a) What finance charge will Jaime pay?

The cash cost is $7500. She decides to finance the project by paying 20% down

Amount paid for down payment = $7500 × 20/100

= $1500

Amount left = $7500 - $1500

= $6000

The balance paid in 36 monthly payments of $189.40.

Hence: $189.40 × 36 = $6818.4

The finance charge = $6818.4 - $6000

= $818.4

(b) What is the APR to the nearest half percent ?

Step 1

Finance charge/ Amount left × 100

= 818.4/6000 × 100

= 13.64

Using the APR table:

The APR to the nearest half percent = 8.5%

what is 0.72 equivalent to?​

Answers

Answer:

18/25

Step-by-step explanation:

Answer:

72%, or, 18/25

Step-by-step explanation:

I just converted 0.72 into a percentage and a fraction. I hope this helps! :P

Change the number below into scientific notation. 3,450,000,000

Answers

Answer:

3.450*10^4

Step-by-step explanation:

3.45x10^9 is the correct answer for scientific notation

10 points
Find the DISTANCE between point (3, -8) and point (-11,5). *

Answers

Answer:

19.1

Step-by-step explanation:

Me after jumping in joy after I found out Netflix is facing criminal charges

Answers

lol same tbh even tho ion  have netflix anymore

If f(x) = 2 + 6x and g(x) = x2 +3 , determine g(4).

Answers

Answer:

The answer is 19.

Step-by-step explanation:

You have to substitute x = 4 into the function of g(x) :

g(x) = x² + 3

g(4) = 4² + 3

g(4) = 16 + 3

g(4) = 19

Charlene Langhorst's gross weekly salary is $680. Her federal withholding is $101.62. Her employer takes out the standard rates for FICA (Social Security/Medicare). The state tax is 1.5% of gross pay. Each week she pays $32.40 for medical insurance. What are Charlene's total weekly deductions? *

Answers

Answer:

Total deductions =  $196.24

Step-by-step explanation:

Gross weekly salary = $680

federal holding = $101.62

FICA standard rate = 7.65% of gross earnings

= 7.65% of $680 = 0.0765 × 680 = $52.02

∴ FICA deductions = $52.02

state tax = 1.5% of gross pay = 1.5% of $680

state tax = 0.015 × 680 = $10.2

∴ state tax = $10.2

Medical insurance = $32.40

Total Deductions = 101.62 + 52.02 + 10.2 + 32.40 = $196.24

plz help me its due soon :( im sad

Answers

Answer:

your answer should be 25 feet

Step-by-step explanation:

Answer:

why are you sad

Step-by-step explanation:

25 ft

Factorise Fully:
21b-3b^2

Answers

See attachment for math work and answer.

EASY INEQUALITIES!!!!

Answers

Answer:

2.16, 3.45

Step-by-step explanation:

Answer:

Hello!!! erz here ^^

Step-by-step explanation:

2.16< [tex]\sqrt{5}[/tex] < 3.45

Hope this helps!! :D

All the comic books in a store are the same price. Vera
buys 3 comic books for $7.50. How much do 5 comic
books cost? How much do 8 comic books cost?

Answers

Answer:

The price for 3 comics is $12.50 and the price for 8 comics is $20.00.

Step-by-step explanation:

To calculate the price of one comic, we can divide the price of the comics by the amount bought:

= $7.50 ÷ 3

= $2.50

Therefore, one comic is $2.50

To figure out how much 5 and 8 comics are, just multiply these numbers by the price of one:

= 5 x $2.50

= $12.50

= 8 x $2.50

= $20.00

The price for 3 comics is $12.50 and the price for 8 comics is $20.00.

A bottled water company charges $8 per month for a water
cooler and $5 per bottle b of water. Write an equation that
represents the total cost C for monthly water service.

Answers

8+5b=c $8 a month added to $5 multiplied by amount of water bottles = the total cost a month

2x + 3y = 6

y = 2/3x - 2
y = 2/3x + 2
y = -2/3x - 2
y = -2/3x + 2

Answers

Answer:

y= −2/3x+2

Step-by-step explanation:

2x+3y=6

Add -2x to both sides.

2x+3y+−2x=6+−2x

3y=−2x+6

Divide both sides by 3.

3y/3=−2x+6/3

3x²-75=0 find the square root​

Answers

Answer:

[tex]x=\pm5[/tex]

Step-by-step explanation:

First, add 75 to each side.

[tex]3x^2-75+75=0+75\\3x^2=75[/tex]

Next, divide each side by 3.

[tex]x^2=25[/tex]

Now, you can take the square root.

[tex]x = \pm\sqrt25}[/tex]

[tex]x=\pm 5[/tex]

The temperature in Monarch, Wisconsin, was -3° F at 6:00 a.m. The temperature rose 12 degrees in 9 hours. What was the temperature in Monarch at 3:00p.m.?​

Answers

Answer:

9 degrees

Step-by-step explanation:

The temperatire was -3 and then rose by 12, -3 + 12 = 9

Other Questions
the floor of a room is in the shape of a square of side 4.8m. the floor is to be covered with square tiles of perimeter 1.2m. Find the cost of covering the floor if each tile costs rupees 27 write the fraction 18/24 in its simplest form Enter an equation to describe the linear relationship.The temperature, y, of a pot of water is 35 F. The temperature increases by 20 F per minute, x, when being heated.The equation is y = Wendy and Mini earn $38 per week for delivering magazines. Wendy worked for x weeks and earned an additional total bonus of $15 Mini worked for y weeks. Which expression shows the total money, in dollars, that Wendy and Mini earned for delivering magazines A: 53x + 38yB: 38 + 15 + 38yC: 38 - 15 + 38yD: 38x + 53y -4x + 6(4x -3)= -8 help im timed Zachary is writing an article that will be included in a Who is most likely Zachary's audience? pamphlet his school is putting together titled "Guide to Your School Library." Zachary's article will explain how to O students about to graduate from the school find information for a science project. O science teachers O parents visiting the school O students who are new to the school what are some similarities between Sparta and Athens how did King George lll react to the olive branch petition sent by the continental congress does anybody know how to solve this equation 5+3104x=20 2. The sum of the measures of the exterior angles of a triangle equals: 60 180 270 360 whats a similarity between jamestown and massachusetts bay How does Napoleon feel about the revolution? Why? I need help with this please Match the following. 1. a formal announcement or written document of an important nature petition 2. a person given the power or authority to act for others delegate 3. a formal request to someone in authority for some privilege, right, or benefit declaration Which sentence from the article provides evidence that professional gaming is a major league sport The company evaluates all projects by applying the IRR Rule. If the appropriate interest rate is 9%, should the company accept this project? You're eating a bowl offruit but you're starting tofeel full. 0. 10. A black hole is a region in space where the gravational poll is so great thatIt can be used to travel to another universe,0It consumes entire galaxies.OLight cannot escapeNew stars are formed, PLEASE HELP, MARKING BRAINLIEST!!!!These triangles are congruent by _____. A. SASB. ASAC. AASD. SSS how do you Convert 50 g to kg in an equation for physics