Find the sum of the first 6 terms of the following series, to the nearest integer.

180, 30, 5, ...

Answers

Answer 1

Answer:

Step-by-step explanation:

First solve for the common ratio:

[tex]\frac{30}{180} = \frac{1}{6} 6 \\ \\\frac{5}{30} = \frac{1}{6}[/tex]

Use the geometric summation equation to solve for sum:

[tex]a(\frac{(1-r^{n} )}{(1-r)})\\180(\frac{(1-\frac{1}{6} ^{6}) }{(1-\frac{1}{6} )}) = \frac{46655}{216} = 216[/tex]

Answer 2

The sum of the first 6 terms of the following series is 540.

What is the geometric series?

A geometric series is the sum of an infinite number of terms that have a constant ratio between successive terms.

The sum of the terms of the geometric sequnece is given by;

[tex]\rm S_n=\dfrac{a(1-r^n)}{1-r}[/tex]

The common ratio of the sequence is;

[tex]\rm \dfrac{a_2}{a_1}=\dfrac{30}{180}=\dfrac{1}{6}\\\\ \dfrac{a_2}{a_1}=\dfrac{5}{30}=\dfrac{1}{6}\\\\[/tex]

The sum of the first 6 terms of the following series is;

[tex]\rm S_n=\dfrac{a(1-r^n)}{1-r}\\\\\rm S_6=\dfrac{180(1-1/6^6)}{1-1/6}\\\\ S_6=\dfrac{180\times 0.99}{5/6}\\\\S_6=\dfrac{180\times 0.99}{0.33}\\\\S_6=\dfrac{178.2}{0.33}\\\\S_6=540\\[/tex]

Hence, the sum of the first 6 terms of the following series is 540.

Learn more about geometric sequence here;

https://brainly.com/question/8934175

#SPJ2


Related Questions

The sides of the base of a right square pyramid and its slant height are tripled. What is the surface area of the larger pyramid divided by the surface area of the smaller pyramid? A. 3 B. 6 C. 9 D. 12

Answers

Answer:

Step-by-step explanation:

If the base length and slant height are multiplied by 3, the surface area is multiplied by 3² = 9

solve the inequality for n.
14 < n - 3​

Answers

Answer:

n > 17

Step-by-step explanation:

Add 3 on both side: n - 3 + 3 > 14 + 3

--> n > 17.

If it is helpful, plz give me Brainliest.

Answer:

n>17

Step-by-step explanation:

14<n-3

move the terms

-n<-3-14

calculate

-n<-17

change the signs and you get n>17

How do you evaluate fuctions?

Answers

Step-by-step explanation: To evaluate functions substitute the given number or expression function's variable.

1 fourth to the 3rd power as a fraction

Answers

Answer:

1/64

Step-by-step explanation:

(1/4)³

1³/4³ = 1/64

(X+5)+(x-5)=56 what does x=?

Answers

Answer:

x=28

Step-by-step explanation:

Step 1: Simplify both sides of the equation.

x+5+x−5=56

x+5+x+−5=56

(x+x)+(5+−5)=56(Combine Like Terms)

2x=56

2x=56

Step 2: Divide both sides by 2.

2x/2=56/2

x=28

plz give me brainiest

Please help ?? I don’t remember how to do this

Answers

Answer:

i hope it help you

Step-by-step explanation:

1) x not equal 3

2) x not equal 5 and greater than or equal 3

3) x greater than or equal 3

4) x not equal 5

which of the following is the correct factorization of the trinomial below -7x^2+5x+12

Answers

The factored form would be (-7x+12)(x+1)

It’s always good to know the several ways to solve these problems, but one of the easiest and fastest would be the box method.

The box method involves you finding you a, b, and c values in a quadratic equation. It goes as follows, Ax^2+bx+c. When doing the box method, you multiply only your A and c. In this case -7*12 which gives you -84. Next you just find you b value (which is 5).

Now comes the trick part, you need to find the factors of -84 that ADD UP to equal 5. Therefore we just find the factors of 84 by listing them (find them for 84 then determine with the negative later). So we have 2, 42/ 3,28/ 4/21/ 6,14 / and 7,12. It becomes easier to find your factor, but 7 and 12 can equal to 5 in this condition due to 84 being negative, therefore one of the factors will be negative. By making 7 negative we can make 12+-7 equal to our b value of 5.

Now that we have the factors, we put them into fractions. We put them in the form that a would be on top and the factor would be on the bottom. Therefore a/(factor). In this case is would be -7/12 and -7/-7. With these fractions, we then simplify as much as we can, -7/12 cannot be simplified so it stays the same, but -7/-7 can be simplified to 1/1.

These fractions then become you FACTORS of your quadratic equation, in which case the a value in the fraction adds x to it, therefore it would be -7x+12 and x+1. The correct would would be (-7x+12)(x+1).

Answer:

-1(7x-12)(x+1)

Step-by-step explanation:

Ape s* x

Find the value of X
2x+40 100

Answers

x= 30.....................

Answer:

x=30

Step-by-step explanation:

how:

so your equation right now is 2x+40=100, so figure this equation out you have to do the opposite so it will be

100-40=60

60/2=30

which makes x=30

hope that helps

please mark as brainliest if correct

thank you

19NBoli

:)

write the equation of a line that has a slope of 3x - 4y = 12 and passes through the point (8, 8)

Answers

first of all we have to find the slope

3x - 4y = 12

-4y = 12 - 3x

y = -3 + ³/₄ x

y = ³/₄x - 3

so the slope is ³/₄

now the equation is :

y-y₁ = m (x-x₁)

y-8 = ³/₄ (x-8)

y-8 = ³/₄ x - 6

y = ³/₄ x -6 + 8

y = ³/₄x + 2

The percent of sales tax is 8% if the skateboard cost $98 what is the total amount you will pay including tax?

Answers

Answer:

The total amount of tax is $7.84, so add that to $98 and you get $105.84 dollars total.

Step-by-step explanation:

Which term matches the definition? one that can be answered with
data and for which it is anticipated that the data collected to answer the
question will vary.
A. symetrical graphs
B. skewed right
C. skewed left
D. statistical question

Answers

D) statistical question

You like math then here

Answers

Answer:

-8b + 9 - 5k

Step-by-step explanation:

I am assuming the blue highlighted portion is your answer, and is not a part of the initial question

(-4b + 15 - 7k) - (6 + 4b - 2k)

Combine like terms

-4b - + 4b

Negative + Positive = Negative

-4b - 4b = -8b

15 - 6 = 9

-7k - - 2k

Negative + Negative = Positive

-7k + 2k = -5k

Put them all together:

0b + 9 - 5k

Simplify

-8b + 9 - 5k

I got the same answer as you (just in a different order)

Ms. White is going to the grocery store to buy peamut butter for $3.50 a jar. She's going to the store with
$35 but needs to save $15 for tomorrow.

Answers

Answer:

5. your question wasnt finished so there was not answer.

Step-by-step explanation:

Im guessing your question was how many jars can she by?

If so then

35 - 15 is 20

20 divided by 3.50 is 5.714

So she only has enough money left to buy 5 whole jars

Find the slope.
Find the y-intercept
Write the equation (y=mx+b)

At Philip’s Phones you can get a new cell phone plan for $45 a month plus $30 activation fee.

Answers

y=45x+30

x=months
y= fee

9514 1404 393

Answer:

slope: 45y-intercept: 30equation: y = 45x + 30

Step-by-step explanation:

The slope is the cost per month. (A slope is often expressed as a ratio: dollars per month, in this case.) The slope is 45.

The y-intercept is the value that obtains when the number of months (in this case) is zero. It is the activation fee, 30. The y-intercept is 30.

__

The equation in slope-intercept form is ...

  y = mx + b . . . . . where m is the slope and b is the y-intercept

Using the above numbers, the equation is ...

  y = 45x + 30

what is 0.24% as a decimal

Answers

Answer:

.0024

Step-by-step explanation:

Hey There!

So when converting a percentage to a decimal all we have to do is move the decimal place over to the left 2 times

so it would be .0024

hope this helps ~ MarkAnswers

Answer:

0.0024

Step-by-step explanation:

0.24% = 0.0024 in decimal form. Percent means 'per 100'. So, 0.24% means 0.24 per 100 or simply 0.24/100.

i hope this helps!! brainliest?

2) Dan is playing a game that involves the spinners shown below.*
10 points
Spinner 1
Spinner 2
Spinner 3
6
2
Greon Red
Blue Yellow
5
3
F
Which durt shows all of die possible combinations of an even number on Spinner 1,
Red or Blue on Spinner 2, and a B on Spinner 3?
A
с
Spinner 1 Spinner 2 Spinner 3
2 Red B
4
Red
B
6 Red B
2 Blu B
Blue B
6 Blue B
Spinner 1 Spinner 2 Spinner 3
2
Rod B
2 Red B
Red
4 Blue
B
6 Blue B
6 Blue B
B
D
CC
Spinner 1 Spinner 2 Spinner 3
1
Red B
2. Blue B
3 Red B
Blue B
5 Rod
B
6
Blue B
Spinner 1 Spinner 2 Spinner 3
2 Red
4 Red
B
6 Red А
2 Blue B
Blue А
6
Blue B

Answers

Answer:

1 spanner 2 greoun red 3 blue 4 .... 6 blue

pls helpppppppppp meeeeeeeeeeeeeeeeeeeeeeeeeeeeeeeee

Answers

I THINK THE ANSWER IS...

people need to stay and tend their crops.

HOPE IT HELPS

Answer:

I think its either A or C but I'm going to go with A

Step-by-step explanation:

Hope this helps (:

answered
I need this done today whoever gets this correct gets brainliest!!! PLZZ HELPP MEE

Answers

The First equation and the Third Equation

are equivalent to 6x - 24.

1) 6 ( x - 4 )

3)3 ( 2x - 8 )

Answer:

first one and third one. hope u get it right!

Step-by-step explanation:

6(x-4)

distribute (6*x and 6*4) then it equals 6x - 24

2(3x - 24) = 6x - 48

3(2x - 8) = 6x - 24

3(3x - 21) = 9x - 63

Help me!?!
I’ll give you 5 stars?!

Answers

Answer:

i think its b 68 because if you add al the sides that what i got

Step-by-step explanation:

18 + 18 + 10 + 10 + 6 + 6=  = 68

Answer:

1080 or 68

Step-by-step explanation: 10*18*6=1080

10+10+18+18+6+6=68

HURRY
An angle measures 47°. What are the measures of the angle’s complement and supplement? A. complement, 43°; supplement, 133° B. complement, 133°; supplement, 43° C. complement, 53°; supplement, 143° D. complement, 143°; supplement, 53°

Answers

The angle that is complementary to 47° is 43°

The supplementary angle of 47 degrees is 133 degrees

Answer:

A.)  complement, 43°; supplement, 133°

Step-by-step explanation:

A compliment angle is any angle(s) that adds up to 90°

A supplement angle is any angle(s) that adds up to 180°

For compliment:

90 - 47 = 43

For supplement:

180 47 = 133

Therefore, the answer would be A.

-kiniwih426

A partir del 1.° de diciembre, un camión de helados visita la calle de Sara cada 3 días y la calle de Ema cada 5 días. ¿Cuáles son los primeros 2 días que el camión visita ambas calles el mismo día?

Answers

Answer:

Los primeros 2 días que el camión visita ambas calles el mismo día es el 15 y 30 de diciembre.

Step-by-step explanation:

Los múltiplos de un número son todos los posibles resultados de multiplicar ese número por todos y cada uno de los números naturales.

Es decir, los múltiplos de un número natural son los números naturales que resultan de multiplicar ese número por otros números naturales.

El conjunto de los múltiplos de un número determinado (salvo el cero) es infinito, pues existen infinitos naturales para multiplicar.

Para determinar cuáles son los primeros 2 días que el camión visita ambas calles el mismo día, debes encontrar los múltiplos de 3 y 5:

múltiplos de 3: 3; 6; 9; 12; 15; 18; 21; 24; 27; 30

múltiplos de 5: 5; 10; 15; 20; 25; 30; 35; 40; 45; 50

Podes observar que los 2 primeros números comunes o que coinciden entre los múltiplos de 3 y 5 son 15 y 30. Esto quiere decir que los primeros 2 días que el camión visita ambas calles el mismo día es el 15 y 30 de diciembre.

A small plant manufactures riding lawn mowers. The plant has fixed costs of GHC48,000 per day and a variable cost of GHC1,400 per unit produced. The mowers are sold for GHC1,800 each. The cost and revenue functions are in that order and , where is the total number of mowers produced and sold each day. How many units must be manufactured and sold each day for the company to break even?

Answers

Answer:

120

Step-by-step explanation:

The break-even point is the point where revenue =cost

48,000+ 1400x = 1800x

48000=400x

X=48000/400

X=120

Equilibrium quantity is 120 mowers

What property is shown below?
129 × 1 = 129
OA.
Commutative Property of Multiplication
OB.
Associative Property of Multiplication
OC. Identity Property of Multiplication
OD
Identity Property of Addition

Answers

Answer:

Associative property of multiplication

Step-by-step explanation:

i need help T^T ill mark brainliestT^T

Answers

Answer:

it's A (I'm sure)

Step-by-step explanation:

........

Answer:

option A is correct 2:10=14:10

Can someone help with this math problem? 3 (x+6) = 27

Answers

Answer:

x = 3

Step-by-step explanation:

Use distributive property: a(b +c) =(a*b) + (a*c)

3(x + 6) = 27

3*x + 3*6 = 27

3x + 18  = 27 {Subtract 18 from both sides}

3x + 18 -18 = 27 - 18

         3x    = 9  {Divide both sides by 3}

        3x/3 = 9/3

x = 3

write the numeral that means the same as "three hundred fifty-two billion, six hundred thirty- five million"

Answers

Answer:

352,635,000

Step-by-step explanation:

Please help thanks I appreciate it! :)

Answers

Answer:

Step-by-step explanation:

120 x .6 =72

120-72 = 48

48x .6 = 28.8

72+28.8 = 100.8

She sold approximately 101 cups of coffee

PLS HELP WILL GIVE BRAINLIEST AND 20 POINTS TY!

Answers

Answer: It is B)

Step-by-step explanation: It was 8.66 something and that rounded to the nearest tenth is 8.7

Answer:

B. 8.7

Step-by-step explanation:

the closest one is but the actual number is 8.6 repeating so 8.7 is correct

Enter the exponential function using t (for time) as the independent variable to model the situation. Then
find the value of the function after the given amount of time.
The value of a textbook is $63 and decreases at a rate of 14% per year for 13 years.
The exponential function that models the situation is y = 63(0.86).
After 13 years, the value of the textbook is $

Answers

Answer:

An exponential function is given by;

f(x)=ba^x

where a is any value greater than 0,

          b is the intial value

when a>1 then f(x) is defined as an exponential growth

when a<1 then f(x) is defined as an exponential decay

From the our function;

f(t)=15000(0.86)^t

a=0.86<1

b=15000

since a<1, the function will be an exponential decay.

Step-by-step explanation:

Solve for A

-2a -12 < -8

How do I do this step by step?

Answers

first you add 12 to the other side and once you have that divide both sides by -2 and since what we’re dividing by is negative the inequality switches so the answer is a > -2
Other Questions
.ASAP HEEEEEEELP TTwTT Company XYZ forecasts expanding markets, see many opportunities for growth, and adopts a growth strategy. It has invested heavily into a highly efficient production process. Administratively, it has tight control over costs and lots of rules and regulations to promote efficiency. According to the adaptation model of strategy, company XYZ:_________a. is a strategie failureb. as prospector c. as defender d. as an analyzer What was a result of the fall of the Western Roman Empire?A. Higher literacyB. Weaker religionC. Smaller citiesD. Centralized rule what is Qanon a lot of people at school keep talking about it but i dont know what it is Question 9What led many Muslims to believe that Ali was the rightful caliph and heir of Muhammad?Ali already ruled a large territory as governor.BAli was the only child of Muhammad and A'isha.Muhammad gave a sermon implying that Ali was chosen.DMuhammad was defeated by Ali at the Battle of the Camel. Help please Ill mark brainliest what is the slant height of a pyramid with surface area of 209 square centimeters and a square base with sides of 7 centimeters? round to the nearest tenth. which would least likely have an impact on global climate changes?Group of answer choices please help!!! thank you!!! Translate the subject pronouns belowyouyou formalheshewey'all in Spainyou allthey can some one help meeeeeee on 17. Macro mineral needed to build strong bones and teethA- ironB -calcium 18. Bodies inability to break down lactose due to absence of the enzyme lactaseA- Lactose IntolerantB- Celiac DiseasePlease HELP ME ITS DUE LIKE RN What features do all right triangles have in common? ATwo legs and a hypotenuseincorrect answer BTwo equal sides and two equal anglesincorrect answer CTwo 90-degree anglesincorrect answer DThree sides of equal length what is the volume of a sphere if the diameter is 21 cm using formula v=4/3 pie (r3). use 3.14 for pie Write the function evens which takes in a queue by reference and changes it to only contain the even elements. That is, if the queue initially contains 3, 6, 1, 7, 8 then after calling odds, the queue will contain 6, 8. Note that the order of the elements in the queue remains the same. For full credit, no additional data structures (queues, stacks, vectors, etc.) should be used. Assume all libraries needed for your implementation have already been included. Find the area of the figure. Find the area of the region enclosed by the graphs of these equations. (CALCULUS HELP) Terrace Corporation makes an industrial cleaner in two sequential departments, Compounding and Drying. All material is added at the beginning of the process in the Compounding Department. Conversion costs are added evenly throughout each process. Terrace uses the weighted average method of process costing. In the Compounding Department, beginning work in process was 3,600 pounds (60% processed), 61,200 pounds were started, 57,600 pounds were transferred out, and ending work in process was 60% processed. Calculate equivalent units for the Compounding Department for August 2016. Terrace Corporation Flow of Units and Equivalent Units Calculation, August 2016 Equivalent Units % WorkConversion % Work done Direct Materials Done Costs Complete/Transferred Ending Inventory Total what are phrasal verbs. please help will give brainliestno wrong answers I NEED HHELP ASAP STOP SENDING ME LINK