Consider the following sequence of numbers.

3,-9,27,-81,...
I need common ratio & sum of 1st five terms

Consider The Following Sequence Of Numbers. 3,-9,27,-81,...I Need Common Ratio & Sum Of 1st Five

Answers

Answer 1

Answer:

Please check the explanation

Step-by-step explanation:

Given the sequence

[tex]3,-9,27,-81,...[/tex]

A geometric sequence has a constant ratio and is defined by

[tex]a_n=a_0\cdot r^{n-1}[/tex]

Computing the ratios of all the adjacent terms

[tex]r=\frac{a_n+1}{a_n}[/tex]

[tex]\frac{-9}{3}=-3,\:\quad \frac{27}{-9}=-3,\:\quad \frac{-81}{27}=-3[/tex]

The ratio of all the adjacent terms is the same and equal to

[tex]r=-3[/tex]

Therefore, the common ratio is:

r = -3

Determining the sum of 1st five terms

As the first element is

[tex]a_1=3[/tex]

[tex]r=-3[/tex]

Geometric sequence sum formula is given by

[tex]a_1\frac{1-r^n}{1-r}[/tex]

Plugin the values

[tex]n=5,\:\spacea_1=3,\:\spacer=-3[/tex]

[tex]a_1\frac{1-r^n}{1-r}=3\cdot \:\frac{1-\left(-3\right)^5}{1-\left(-3\right)}[/tex]

            [tex]=3\cdot \frac{1-\left(-3\right)^5}{1+3}[/tex]

             [tex]=\frac{\left(1-\left(-3\right)^5\right)\cdot \:3}{1+3}[/tex]

             [tex]=\frac{732}{1+3}[/tex]       ∵

             [tex]=\frac{732}{4}[/tex]

              [tex]=183[/tex]

Therefore, the sum of the first five terms of the sequence is: 183        


Related Questions

Solve. | 2x + 4 | = 10

Answers

Answer:

Answer in screenshot that is provided.

Step-by-step explanation:

Here is a linear equation, y = 1x +
5
Are (1, 1.5) and (12, 4) solutions to the equation? Why or why not?

Answers

Answer:

Step-by-step explanation:

plug in both values and see if the equations are true

1.5 = 1(1) + 5

1.5 = 1 + 5

1.5 does not equal 6

so (1,1.5) is not a solution

4 = 1(12) + 5

4 = 12 + 5

4 does not equal 17

so (12,4) is not a solution

Answer:

Just test the points in the equationPoint 1: (1,1.5)[tex]y=x+5\\(1.5)=(1)+5\\1.5=6[/tex] ?? Is that true? No, so this point is not a solutionPoint 2: (12,4)[tex]y=x+5\\(4)=12+5\\4=17[/tex] ?? Not true, its not a solution.so neither is a solution because the equation is not satisfied

You made 15 t-shirts for beta club. A t-shirt box will hold 5 t-shirts. How many boxes do you need for all the shirts? 10 points A) 5 B) 15 C) 20 D) 3

Answers

Answer:

D) 3

Step-by-step explanation:

15 divided by 5 equals 3.. brainliest plz

If there’s 15 shirts and a box holds 5, there’s 3 boxes. 15:5=3. So the answer is D.

1 inch : 12feet. if the actual width of the tent is 36 feet how wide is the tent.​

Answers

Answer:

If the actual width is 36 feet, then the tent is 3 inches wide in scale.

Step-by-step explanation:

Let x be the width in inches.

The scale is: 1 inch : 12feet. The scale can be represented as inches to feet ratio and then equivalent ratios will be used

This can be expressed as fraction as 1/12

The equivalent ratios are:

[tex]\frac{1}{12} = \frac{x}{36}\\\frac{36}{12} = x\\x = 3[/tex]

Hence,

If the actual width is 36 feet, then the tent is 3 inches wide in scale.

The area of a circle is 36n units squared.
What is the radius?

Answers

Answer:

3.385137501

OR it is 1.909859317

Step-by-step explanation:

for the first one:

36/pi which is 11.4591559, then you take the square root of 11.4591559 to get 3.385137501

For the second:

you take the square root of 36 which is 6, then you divide 6 by pi which gets you 1.909859317

BUT NOT 100% SURE THIS IS CORRECT!

The solutions to the equation f(x) = g(x) are -2 and 1. Iff and g are graphed on the same coordinate plane, which statement must be true?
The functions will intersect at x = -2 and x = 1.
The functions will intersect at y = -2 and y = 1.
Both functions will have y-intercepts at 2 and 1.
Both functions will have x-intercepts at -2 and 1.

Answers

Answer:

The correct option is;

The function will intersect at x = -2 and x = 1

Step-by-step explanation:

The question parameters are

The functions in the question are f(x) and g(x)

The solution to the equation f(x) = g(x) are -2, and 1

Given that the equations, f(x) and g(x), are both given in values of x, their solution will be the x values that satisfies both functions

Therefore, the functions will intersect (have the same values of f(x) and g(x)) at the points of the solutions, which are given as x = -2, and x = 1

The statement that should be true is the function will intersect at x = -2 and x = 1.

Given that,

The solutions to the equation f(x) = g(x) are -2 and 1. If f and g are graphed on the same coordinate plane.

Based on the above information, the following information should be considered:

As the solutions represent x values that satisfied the both functions. Also, the functions should intersect that contains the same value i.e. x = -2 and x = 1.

Therefore, we can conclude that the first option is correct.

Learn more: brainly.com/question/24169758

 

a solution of x2 + 5x = −2

Answers

Answer:

You could solve this equation by referring to the quadratic equation

x=-5+/-√17/2

Step-by-step explanation:

A train traveled 252 miles in 4 hours at a constant speed through Norway. How far did the train travel per hour?

Answers

Answer:

63

Step-by-step explanation:

252/4 is 63

Answer: The train traveled 63 miles per hour

Step-by-step explanation:

252/4=63

a triangle has side lengths of 14, 23, and 27. Is it a right angle ?

Answers

Answer:

No, it is not

Step-by-step explanation:

Here, we want to check if the lenghts given is that of a right angle triangle

For a right angle triangle, the square of the hypotenuse is equal to the sum of the squares of the two other sides

The hypotenuse represents the longest side

So 27^2 = 14^2 + 23^2

The difference between these is 4, and as such the triangle is not a right angled


Solve each system of equations.
1. Solve:
X-y=1
2x + y = 8
Solution
* write your answer as an ordered pair (X,Y)

Answers

Answer: {x,y} = {10,-2}

Step-by-step explanation: {x,y} = {10,-2}

HELP PLZZ
Which policy was supported by the Federalists, but not the Democratic-Republicans?

Answers

Answer:

I think it was the creation of a national bank? They didn't want to centralize their economy and give more power to the federal government.

the person above me is 100% correct

Step-by-step explanation:

1. One number added to three times another number is 24. Five times the first num
three times the other number is 36. Find the numbers.

Answers

Answer:

Let x equal the one number.

Let y equal the other number.

x + 3y = 24

5x +3y = 36

Subtract the first equation from the second equation.

4x = 12

x = 3

Upvote

0

Downvote

Comments

3

What is the ratio 18:6 simplified

Answers

Answer:

18/6 = 3/1 = 3

Step-by-step explanation:

Simplify 18/6 reduces the fraction 18/6 to the lowest form. You can change the numerator or denominator to simplify any other fraction.

How many solutions does the equation 4x + 8 = −2 − 2 + 5x have? (1 point) Two One None Infinitely many

Answers

Answer:

one

Step-by-step explanation:

only one value of x will let this equal. two would mean its exponential, none would mean the number before x would be the same on both sides but with different numbers for example 5x-8=5x+2. same 5x but when cancel them out -8 = 2 which is false. infinitely many means the two sides are identical.

Answer:

there are zero answers

Step-by-step explanation:

Quadrilateral DEFG - quadrilateral KLMN. Find the given angle measure.

Answers

Answer:

76

Step-by-step explanation:

Evaluate 12 divided by (-3)(2) + 5. a) -13 b) 3 c) -3

Answers

Answer:

B

Step-by-step explanation:

12 divided by -6 is -2, plus 5 is 3

:D

What is 63.63 repeating as a fraction

Answers

Answer:

x = 700/11

Step-by-step explanation:

let x = 63.63...(by repeating i assume you mean the 63 is repeated as 63.636363...)

therefore 100x = 6363.63..

100x-x =6300 (the recurring bit has been cancelled out which is what you should always aim to do)  

99x=6300

x = 6300/99  

cancel down

x = 700/11

hope that helps! :)

Maggie sold 30 boxes of cookies in 6 days. How many days will it take her to sell 100 boxes of cookies?

Answers

Answer:

If maggie sold 30 boxes of cookies in 6days, how long will it take her to collect 100 boxes

10

Step-by-step explanation:

By Comparison:

100 ÷ 30 = 3.3333333333333

Then we must have:

x ÷ 6 = 3.3333333333333

Solving for x,

x = 6 × 3.3333333333333

x = 20

By Cross Product:

(30/6) = (100/x)

The Cross Product:

(30 * x) = (100 * 6)

Solving for x:

x = (100 * 6) / 30

Answer:

It will take her 20 days to sell 100 boxes of cookies.

Step-by-step explanation:

30 boxes = 6 days

100 boxes = [tex]\frac{100}{30}[/tex] × 6

                 = 20 days

The table shows the number of miles driven over time.

Answers

I think I could possibly be C

50 POINTS!!! WILL MARK BRAINLIEST!!!
solve numbers 16 and 18
show work please

Answers

Answer:

16) 102°18) 75°

Step-by-step explanation:

16)

∠QPR = 1/2(QR + SV)

26x - 2 = 1/2(131 + 18x + 1)26x - 2 = 66 + 9x26x - 9x = 66 + 217x = 68x = 68/17x = 4

∠QPR = 26*4 - 2 = 102°

18)

mBC = ?

∠BAC = 1/2(mBC + mFD)

8x + 6 = 1/2(8x + 11 + 9x - 7)8x + 6 = 1/2(17x + 4)16x + 12 = 17x + 417x - 16x = 12 - 4x = 8

mBC = 8*8 + 11 = 75°

angle 9 and angle 10 are corresponding and complementary angles formed by two parallel lines cut by a transversal. Find the measure of angle 9.​

Answers

Answer:

45 Degrees

Step-by-step explanation:

9 and 10 are corresponding meaning that they will be the same. They are also complementary, so they equal 90 degrees when added. 90/2 is 45.

Teresa measures five eighths foot of ribbon for a costume. She needs seven pieces of ribbon with that same length. What is the total length of ribbon Teresa needs to make all the costumes?

Answers

Answer:

[tex]Total\ Length = \frac{35}{8}\ ft[/tex]

Step-by-step explanation:

Given

[tex]Length = \frac{5}{8}\ ft[/tex]

[tex]Number = 7[/tex]

Required

Determine the total length

Since, he ribbons are of the same lengths.

The total length is calculated as:

[tex]Total\ Length = Length * Number[/tex]

[tex]Total\ Length = \frac{5}{8}\ ft * 7[/tex]

[tex]Total\ Length = \frac{5 * 7}{8}\ ft[/tex]

[tex]Total\ Length = \frac{35}{8}\ ft[/tex]

c

Step-by-step explanation:

Teresa measures five eighths foot of ribbon for a costume. She needs seven pieces of ribbon with that same length. What is the total length of ribbon Teresa needs to make all the costumes? (2 points)

a

one and four eighths feet

b

two and three fifths feet

c

four and three eighths feet

d

five and two fifths feet

HELP JUST LOOK AT PICTURE

Answers

It should be A and C

Which of the following lines is not parallel to the graph of y= 3x + 9
a.
3x - y = 10
c.
3y - x = 10
b.
y - 3x=11
d.
6x - 2y = 10

Please select the best answer from the choices provided

Answers

Answer:

a 3x - y = 10, b y - 3x=11, and d 6x - 2y = 10, are parallel.

Answer:

c. 3y - x = 10

Step-by-step explanation:

The slope-intercept form of a line

The equation of the line in the slope-intercept form is:

y = mx + b

Here, m the slope and b the y-intercept.

To compare the slope of different lines, we should write them in the above form and compare their values of m.

The given line is:

y = 3x + 9

The slope of this line is m=3

Any parallel line must have the very same value of m.

None of the following options can be directly compared because they are not in the slope-intercept form, so they must be converted.

a. 3x - y = 10

Solving for y:

- y = 10 -3x

y = 3x - 10

The slope of this line is m=3, thus this line is parallel to the given line

c. 3y - x = 10

Solving for y:

3y = x + 10

y = 1/3 x - 10

The slope of this line is m=1/3, thus this line is NOT parallel to the given line

b. y - 3x = 11

Solving for y:

y = 3x + 11

The slope of this line is m=3, thus this line is parallel to the given line

d. 6x - 2y = 10

Solving for y:

- 2y = -6x + 10

Dividing by -2:

y = 3x - 5

The slope of this line is m=3, thus this line is parallel to the given line

Answer: c. 3y - x = 10

Just want a friend
Hi

Answers

Answer:

Meeeeeeee, I want to be your FRIEND!!! I don't have any.

I love friends and it's always nice to have someone that has your back at all times. It's also nice to have someone who shares the greatest moments with you and someone who truly cares for you. I can be your friend if you want to, but you don't have to accept me as a friend if you don't want to, but either way please don't judge this message. I didn't do it because I like you, I did it to be a nice person. Hope you're having a wonderful afternoon and have fun. Enjoy the last day of your Thanksgiving Break!!! ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️ ☺️

The domain, range, and intercepts of a function are shown. Which set of information could be characteristics of the function's inverse? domain: x ≥ -1 range: y ≥ -2 y-intercept: (0,-1) x-intercept: (1,0)

Answers

Just took the test so ik it's right

Domain: x is greater than or = to -2

Range: y is greater than or = to -1

Y-int: (0-1)

X-int: (-1,0)

Basically you just flip everything

Answer:look at explanation

Step-by-step explanation:

A 2-column table with 4 rows. Column 1 is labeled Gallons with entries 2, 4, b, 10. Column 2 is labeled miles with entries 56, a, 168, c.
Alexa is planning to drive across the United States in her car. She started making a table to represent the proportional relationship between gallons of gas and miles driven. The table shows how far she can travel for each gallon of gas that she uses.

What is the constant of proportionality?
miles per gallon

Answers

Gallons | Miles
2 | 56
4 | a
B | 168
10 | c

If he can go 56 miles with 2 gallons then he can travel 28 miles with 1 gallon.
4 • 28 = a = 112
168/28=b=6
10 • 28 = c = 280
The constant of proportionality of miles per gallon is 28
Can I get brainliest pls

Answer:

Gallons | Miles

2 | 56

4 | a

B | 168

10 | c

Step-by-step explanation:

Please help math experts need your help 15 points !

For number 2 the Awnser choices are

3
-3
5
-5

Answers

Answer:

12 = -3 - 3x

Step-by-step explanation:

Same concept as the last question I answered. First, let's derive a formula from the given model. So we have 3 negative x and 3 negative 1 which equal to 12 positive ones, this can be written as:

-3x - 3 = 12

which can be rewritten as

12 = -3 - 3x

Aimee is in charge of buying tickets for a trip to the movies. She can buy tickets at the theater or online. At the theater, 8 tickets cost $60. Online, 6 tickets cost $51. Aimee needs to buy 24 tickets. How much money can Aimee save by buying tickets at the lower price? Show your work

Answers

Answer:

Aimee can save $24 by buying tickets at the lower price that is at the theater.

Step-by-step explanation:

First, you need to find the amount she would spent by buying tickets at the theater and online by using a rule of three:

Theater:

60→8

x  ←24

x=(60*24)/8=180

Online:

51→6

x ←24

x=(51*24)/6=204

Now, you need to calculate the difference:

$204-$180=$24

According to this, the answer is that Aimee can save $24 by buying tickets at the lower price that is at the theater.

Answer:

Aimee can save $24 by buying tickets at the lower price that is at the theater.

Katherine has $140 in the bank and is saving $6 per week. Abbie has $462 in the bank, but spending at a rate of $10m per week. Which equation will determine when they will have the same amount of money in the bank?
A). 140+6x=462+10x
B). 140+6x=462-10x
C). 140+10x=462-6x
D). 140-6x=462+10x

Answers

140 + 6x = 462 - 10x

Hope I helped

Have a great day

Other Questions
Question 1 of 1Match the color of each sign with the type of information it provides. (45 points)1: YellowA. Recreational and cultural-interest guidance2: Fluorescent Yellow-GreenB. Regulatorinformationy3: OrangeC. General warning or caution4: GreenD. Motorist services guidanceC 5. BrownE. Warning6: BlueF. Stop or prohibition7: RedG. Incident management8: Black & WhiteH. Directional guidance or navigation; indicates movement is permittedC 9: Fluorescent PinkI. Temporary work zone why do you think states have licensing requirements for certain occupations? How could Thomas Paines argument have been used to convince colonists to declare independence from Great Britain? whats the difference between spring tides and neap tides What is Zirconium-78 protons and neutrons? The Case of the Missing Mass: Students have completed the experiment of combining vinegar and baking soda. They notice that their beginning mass in the video does not match the ending one. Use the equation(below) and the Law of Conservation of Mass to explain why the students have NOT destroyed atoms in their experiment. This is the chemical equation for the experiment: "A Valentine"by Edgar Allan PoeFor her this rhyme is penned whose luminous eyes,Brightly expressive as the twins of Leda,Shall find her own sweet name, that nestling liesUpon the page, enwrapped from every reader.Search narrowly the lines!they hold a treasureDivinea talismanan amuletThat must be worn at heart. Search well the measureThe wordsthe syllables! Do not forgetThe trivialest point, or you may lose your laborAnd yet there is in this no Gordian knotWhich one might not undo without a sabre,If one could merely comprehend the plot.Enwritten upon the leaf where now are peeringEyes scintillating soul, there lie perdusThree eloquent words oft uttered in the hearingOf poets, by poetsas the name is a poet's, too,Its letters, although naturally lyingLike the knight PintoMendez FerdinandoStill form a synonym for TruthCease trying!You will not read the riddle, though you do the best you can do.Based on the words luminous, treasure, search, lose, scintillating, and riddle that are used in the poem, what does the poet think of love? Precious but mysterious Short-lived and fickle Understandable but strange Well-worn and comfortable When is the last day you can send in federal income tax forms?june 15july 15april 15 november 15 According to Hatfield, which kind of love is about caring and intertwining yourlife?A. AttachmentB. Intimate loveC. Passionate loveD. Companionate love Which of these statements about Jessamine and Nathaniel is supported by the story The fastest elevators in the Burj Khalifa can travel 330 feet in just 10 seconds How fast does the elevator go in 1 foot? Help me! Ill mark you brainly! Which is true about the Athenians?Which is true about the Athenians? They grew poor as a result of Pericles' battle strategies. They grew rich as a result of Pericles' battle strategies. They grew poor as a result of the Delian League. They grew rich as a result of the Delian League. What is -6y + 3 = 3? Find the value of x.28 Leslie can buy her dog's food at Petco for $25 and receive 9 packs with four cans in each. Leslie can buy the same food at Petsmart for the same price with 7 packs of six cans in each. Which store should Leslie buy her dog food from? HELP ME PLEASE ASAP?!?!What is the area of the obtuse triangle given below? Where is Sans :< Plz help me find Sans Hummans The value of a mountain bike y (in dollars) can be approximated by the model y=200(0.75)t, where t is the number of years since the bike was new.Would this table show growth or a decline (decay)? How do you know?Identify the annual percent increase or decrease in the value of the bike.Estimate when the value of the bike will be $50. What is the enthalpy for reaction 1 reversed?reaction 1 reversed: N2O4N2 + 2O2Express your answer numerically in kilojoules per mole.