7) Given that Sn=3-2^(-4n)
is the sum of the first n terms of a sequence.
Un is the n term.
a) Express Un+1 in terms of n.
b) Deduce that the
sequence is a geometric progression.

Answers

Answer 1

Answer:

Step-by-step explanation:

[tex]s_{n}=3-2^{-4n}\\s_{n+1}=3-2^{-4(n+1)}=3-2^{-4n} *2^{-4}\\s_{n+1}-s_{n}=3-2^{-4n}*2^-4-3+2^{-4n}[/tex]

[tex]=2^{-4n}-2^{-4n}*2^{-4}\\=2^{-4n}(1-2^{-4})\\=2^{-4n}(\frac{2^4-1}{2^4})\\=2^{-4n}\frac{15}{16}\\U_{n+1}=15*2^{-4(n+1)}[/tex]


Related Questions

What is the total amount of material
needed for the entire birdhouse?

Answers

Answer:

This question is incomplete ... plz complete the question so that you may get better help.

Step-by-step explanation:

From: Brainy services

plsssssss on thissss i need someone helppp plssss helppp

Answers

Answer:

B

Step-by-step explanation:

A is incorrect, the y-axis represents the distance, not time

What is the percent of increase for a population that changed from 25000 to 30000

Answers

The population has increased by 20 percent

The percent of increase for a population that changed from 25,000 to 30,000 will be 20%.

What is the percentage?

The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates for one hundred percent. It is symbolized by the character '%'.

The percentage is given as,

Percentage (P) = [Final value - Initial value] / Initial value x 100

The population changed from 25,000 to 30,000. Then the percentage is calculated as,

P = [(30,000 - 25,000) / 25,000] x 100

P = (5,000 / 25,000) x 100

P = 0.20 x 100

P = 20%

The percent of increase for a population that changed from 25,000 to 30,000 will be 20%.

More about the percentage link is given below.

https://brainly.com/question/8011401

#SPJ5

Two friends each choose a slice of pizza with one topping. The available
toppings are pepperoni (P), onions (O), meatballs (M) and sausage (S).
Write an organized list using the format (Friend 1. Friend 2) to represent
the sample space of toppings chosen between the two friends.​

Answers

Answer:

Sample space: PP, PO, PM, PS, OP, OO, OM, OS, MP, MO, MM, MS, SP, SO, SM, SS.

Step-by-step explanation:

Suppose Friend 1 select pepperoni, then Friend 2 can choose between 4 options. This gives us 4 possibilities. Then, for each selection made by Friend 1, there are 4 possibilities, given that Friend 1 has 4 different options,  the sample space consists of 16 outcomes.

Does (7, 1) make the equation y = x true?

Answers

Answer:

No.

Step-by-step explanation:

The point (7,1) contains a x-value of 7 and a y-value of 1.  7 does not equal 1.

Answer:

The equation is true.

Step-by-step explanation:

Rewrite using a negative exponent.
1/a ^4

Answers

Answer: a^-4

Step-by-step explanation:

  [tex]\frac{1-4}{a^4-4}[/tex]  = a^-4

At Work-It-Out, a gym membership is $50 per month with no registration fee. At Get Fit, the registration fee is $100 and membership costs $30 per month. Which equation could be used to find the number of months, m, for which the total cost of both gyms is the same? 100+30m=50m 50m=30+100m 100+50m=30m 50m=100−30m

Answers

Answer:

Step-by-step explanation:

50x=30x+100

The equation is 100 + 30m = 50m and the no. of months for which total cost of both the gyms will be same is 5 months.

What is a linear equation ?

A linear equation is an algebraic equation in which a variable has a highest degree of 1.

According to the given question At Work-It-Out, a gym membership is $50 per month with no registration fee and At Get Fit, the registration fee is $100 and membership costs $30 per month.

Given no. of months is m.

∴ 50m = 30m + 100

50m - 30m = 100.

20m = 100

m = 5.

learn more about linear equation here :

https://brainly.com/question/13738061

#SPJ2

What is the rule that describes the numbers in this pattern?
-10,000; -1,000; -100; -10; -1; -0.1; -0.01; -0.001
A Each number is 10 more than the number to its left.
B Each number is one-tenth the number to its left.
C Each number is one-tenth the number to its right.
D Each number is 10 times the number to its left.

Answers

Answer: C Each number is one-tenth the number to its right.

Step-by-step explanation: Just count the number to the right each time.


Which equation describes the circle with center (5, -1) and
radius 4?

Answers

Answer:

[tex](x-5)^2+(y+1)^2=4^2[/tex]

Step-by-step explanation:

The equation is: [tex](x-h)^2+(y-k)^2=r^2[/tex]

(h, k) = center.

[tex](x-5)^2+(y+1)^2=4^2[/tex]

Points are plotted at (-2, 2), (-2,4), and (2,-4). A fourth point is drawn such that the four points can be connected to form
a rectangle. What is the area of this rectangle?
8 square units
12 square units
16 square units
24 square units

Answers

The area is 24 square units

Which statement describes the graph of h (x)?

Answers

Answer:

The 4th option

Step-by-step explanation:

-3 will make you go down

What is the answer I need the answer

Answers

Answer:

The correct choice is A

Step-by-step explanation:

the definition of inverse is the opposite of something or different in direction so that would mean they want you to switch what they gave you so that would mean the answer is choice A

I will give brainliest answer and upvote

Answers

Answer:

397.39

Step-by-step explanation:

steps are all stated in the picture, basically use area of circle minus area of rectangle will give you the shaded area

If Lebron can run 12 laps in 2 hours, approximately how long will it take him to run 60 laps?

Answers

Answer:

10 hours

Step-by-step explanation:

Let's set up a proportion using the following setup.

hours/laps=hours/laps

We know that it takes him 2 hours to run 12 laps. We don't know how long it will take him to run 60 laps, so we can say it takes x hours to run 60 laps.

2 hours/12 laps=x hours/60 laps

2/12=x/60

We want to find out what x is. In order to do this, we have to get x by itself. Perform the opposite of what is being done to the equation. Keep in mind, everything done to one side, has to be done to the other.

x is being divided by 60. The opposite of division is multiplication, so multiply both sides by 60.

60*2/12=x/60*60

60*2/12=x

10=x

It will take Lebron 10 hours to run 60 laps.

What is 25% of $4007

Answers

Answer:

$1001.75

Step-by-step explanation:

Do 4007 x 0. 25 on a calculator

Give the domain and range.

Answers

Answer:

Domain is {-2,0,2}

Range is {4,6,8}

Step-by-step explanation:

The domain is the input or x values

Domain is {-2,0,2}

The range is the output or y values

Range is {4,6,8}

Simplify ^4 sqrt 16x^8y^12z^4

Answers

Answer:

Step-by-step explanation:

[tex]y^{4}\sqrt{16x^{8}y^{12}z^{4}}=y^{4}\sqrt{4*4*x^{4*2}y^{6*2}z^{2*2}}\\\\ =y^{4}\sqrt{4^{2}*(x^{4})^{2}*(y^{6})^{2}*(z^{2})^{2}}\\\\=y^{4}*4*x^{4}*y^{6}*z^{2}\\\\=4x^{4}y^{4+6}z^{2}\\\\\\=4x^{4}y^{10}z^{2}[/tex]

Since it is a ratio of two integers,
6/4 is irrational

Answers

Answer:

is this a question? also, 6/4 is not irrational, it is rational, and an irrational number is a number that cannot be expressed as a ratio of two integers, aka a simple fraction

The number of bricklayers needed to build a brick wall varies inversely as the number of hours needed. Four bricklayers can build a brick wall in 30 hours. How long would it take 5 bricklayers to build a wall?

Answers

Answer: 24 hours

Step-by-step explanation:

You multiply 30 by 4/5, since this is inverse.

If it took 4 bricklayers to build a brick wall in 30 hours, then it would 24 hours for 5 bricklayers to build a brick wall.

The amount of time is reduced down to 4/5 of the first time because there are now 5 bricklayers instead of four.

Answer:

It would take 24 hours for 5 bricklayers to build a wall.

Step-by-step explanation:

We can deduce the number of hours the bricklayers needed to build a wall because they are inversely proportional.

In other words, more bricklayers will result in fewer work hours.

4 bricklayers × 30 hours = 120 bricklayers hours

120 bricklayers hours / 5 bricklayers = 24 hours

Therefore, it would only take 24 hours for 5 bricklayers to build a wall. (Which is 6 hours faster since one person joined the workforce to help the others).

I hope this helps!

Simplify.
(3.8w+ 4) – 1.5w+8
2.3 w+ 12
5.3 w+ 12
2.3 w-12
5.3 w-12

Answers

Answer:

2.3w +12

Step-by-step explanation:

(3.8w+ 4) – 1.5w+8

Combine like terms

3.8w-1.5w   +4+8

2.3w +12

Answer:

2.3w+12

Step-by-step explanation:

Parentheses do not matter for this question.

(3.8w+ 4)–1.5w+8=

3.8w+4-1.5w+8=

Subtract 1.5w from 3.8w

2.3w+4+8=

Add 4 and 8 together

2.3w+12

5. A model of Earth is located 7600 meters from the Globe Arena in Sweden’s solar system model. The volume of the model is approximately 3052.08 cubic centimeters. What is the length of the radius of the

Earth model?

Solve each problem. Use 3.14 for p.

Answers

Answer:

the length of the radius of the Earth Model = 9cm

Step-by-step explanation:

The volume of the model of Earth is approximately 3052.08 cubic centimeters.

It has been discovered that the Earth is spherical in shape, hence this model is spherical as well.

The formula for the Volume of a Sphere = 4/3 πr³

Where r = radius or the length of the radius

The Volume of the Earth Model = 3052.08 cm³

We are told to use π = 3.14

To find the length of the radius, we have derive the formula

V = 4/3 × π × r³

V = 4πr³/3

Cross multiply

3V = 4πr³

Divide both side by 4π

3V/4π = r³

We find the cube root of both sides =

∛(3V/4π) = r

Substituting our given values in the question, we have:

∛(3 × 3052.08/ 4 ×3.14) = r

r = ∛9156.24÷12.56

r = ∛729

r = 9cm

Therefore, the length of the radius of the Earth Model = 9cm

The graph below shows the average daily temperatures on January 1 from 1900 to 1934 for city A. A graph shows the average daily temperature on the x-axis, and number of years on the y-axis, from 1 to 4. The average temperature was 18 for 2 years; 19 for 3 years; 20 for 2 years; 21 for 3 years; 22 for 2 years; 23 for 4 years; 24 for 3 years; 25 for 3 years; 26 for 5 years; 27 for 2 years; 28 for 1 year; 29 for 2 years; 30 for 2 years; 31 for 1 year. The mean of the temperatures in the chart is 24° with a standard deviation of 4°. Which temperature is within one standard deviation of the mean? 18° 19° 22° 30°

Answers

The temperature which is within one standard deviation of the mean is 22 degree Celsius of the graph of average daily temperatures.

What is the mean and standard deviation of data?

The mean of the data is the average value of the given data.The standard deviation of the data is the half of the difference of the highest value and mean of the data set.

The graph below in the attached image shows the average daily temperatures on January 1 from 1900 to 1934 for city A.

A graph shows the average daily temperature on the x-axis, and number of years on the y-axis, from 1 to 4.

Interval within 1 standard deviation of the mean when the mean is μ and standard deviation σ can be given as,

[tex][\mu-\sigma, \mu+\sigma][/tex]

The mean of the temperatures in the chart is 24°, with a standard deviation of 4°. Put these values,

[tex][\mu-\sigma, \mu+\sigma]\\\ [24-4, 24+4]\\\ [20, 28][/tex]

The temperatures in the options given will be correct, which lies in the above range.

Thus, the temperature which is within one standard deviation of the mean is 22 degree Celsius of the graph of average daily temperatures.

Learn more about the mean here;

https://brainly.com/question/14532771

Answer:

C

Step-by-step explanation:

Took the quiz got a 100%

Help!
MJ Supply distributes bags of dog food to pet stores. Its markup rate is 28%. Which equation represents the new price of a bag, y, given an original price, p? Select all that apply. *
A) y = 0.72p
B) y = p + 0.72p
C) y = 1.28p
D) y = p + .28p
E) y=1.28p
F) y = 1 + .28p

Answers

Answer: it’s C.

Step-by-step explanation:

The equation that represents the new price of a bag is y = 1.28p.

Markup rate is the ratio of the difference between the selling price and cost price to the cost price. It is given by:

Markup rate = (selling price - cost price)/cost price

Given that y is the selling price, p is the cost price and the markup rate is 28%, hence:

28% = (y- p)/p

y-p = 0.28p

y = 1.28p

Hence the equation that represents the new price of a bag is y = 1.28p.

Find out more at: https://brainly.com/question/23106860

What are the lines in the picture parallel ?

A. They both lie in the same plane
B. They both travel on forever and ever
C. They are both the same size
D. They are equal width apart, travel in the same direction, and never meet.

Please help me with this

Answers

I think it’s D because they are never going to touch

The lines in the picture parallel because they are equal width apart , option (D) is correct.

What are parallel lines?

Two straight lines in a plane such that even on getting extend till infinity they do not intersect each other and always at same distance from each other .

In the given picture the red line and black lines appears to have same distance between them .They are parallel not only because they are coplanar as coplanar lines can intersect each other.

Two lines travelling to infinity need not to be parallel always as they can intersect at some point and still travel to infinity.

If two lines of same size are there still they can have different perpendicular distance between them at diff points, they can be slightly tilted towards each other . Therefore they need not be parallel when they are of same size. And given lines are infinite therefore we cannot say that they are of same size also.

If two lines are equal width apart and never meet then it means the distance between them is always same therefore they are parallel,

Therefore, the lines in the  picture are parallel because they are equal width apart option (d) is correct.

Also, Learn more about the parallel lines from the given below link:

https://brainly.com/question/19714372

#SPJ5

Help my please please

Answers

Answer:

Rectangle:6+5=11(Odd)

Triangle:6+6=12(even)

Star:4+3=7(odd)

Pentagon:9+8=17(odd)

Hexagon:6+6+12(even)

Circle:4+4=8(even)

Step-by-step explanation:

Hope this helps:)

Answer:

odd, even

odd, odd

even, even

Step-by-step explanation:

Number the pictures starting from left to right and the down, then pictures 1, 3 4 are odd

2, 5, 6 are even.

What is the slope of the line represented by the equation y + 3 = -4(x - 5)?

Answers

Answer:

-4

Step-by-step explanation:

The point slope form of a line is

y-y1 = m(x-x1)

Where m is the slope and (x1,y1) is a point on the line

y + 3 = -4(x - 5)

The slope is -4

Which best describes the triangle

Answers

Answer:

Acute and isoselces

Step-by-step explanation:

Isoseles triangles have two sides of equal length. Acute triangles' angles are all less than 90°.

The best describes the triangle is the acute and isosceles.

We have given that the triangle

We have to describe the given triangle

What is the isosceles triangle?

An isosceles triangle is a triangle that has two sides of equal length. Sometimes it is specified as having exactly two sides of equal length, and sometimes as having at least two sides of equal length, the latter version thus including the equilateral triangle as a special case.

Isosceles triangles have two sides of equal length. Acute triangle angles are all less than 90°.

To learn more about the triangle visit:

https://brainly.com/question/17335144

#SPJ2

question in attachment

Answers

Answer:

[tex]a_{1}=6[/tex]

Step-by-step explanation:

It is sum of arithmetic progression

[tex]$S_{20}=\frac{20}{2} [2a_{1}+(20-1)\cdot 4]$[/tex]

[tex]$880=10[2a_{1}+(19)\cdot 4]$[/tex]

[tex]$880=10[2a_{1}+76]$[/tex]

[tex]880=20a_{1}+760[/tex]

[tex]120=20a_{1}[/tex]

[tex]a_{1}=6[/tex]

Simplify 2(x - 4) + 7(x + 2). 9x + 6 9x - 4 9x - 6

Answers

Answer:

-The final answer is [tex]9x + 6[/tex] .

Step-by-step explanation:

Simplify the following equation:

[tex]2(x - 4) + 7(x + 2)[/tex]

-Use Distributive Property:

[tex]2(x - 4) + 7(x + 2)[/tex]

[tex]2x - 8 + 7x + 14[/tex]

-Combine [tex]2x[/tex] and [tex]7x[/tex] together:

[tex]2x - 8 + 7x + 14[/tex]

[tex]9x - 8 + 14[/tex]

Add [tex]-8[/tex] and [tex]14[/tex] together:

[tex]9x - 8 + 14[/tex]

[tex]9x + 6[/tex]

So, the final answer is [tex]9x + 6[/tex] .

2x-8+7x+14+9x+69x-49x-6
2x+7x+9x+69x-49x+14-6
38x+8
Plz mark brainiest
Hope this helpers

Twice a certain number is tripled. The resulting number is _____. 2x + 3 2x - 3 (2x)3 (2x)

Answers

Answer:

(2x)3

Step-by-step explanation:

Twice a certain number is tripled. Use x as the unknown number and double it.

2x

Now triple the whole answer

(2x)3

Answer:

[tex](2x)3[/tex]

Step-by-step explanation:

Let's say [tex]x[/tex] is the number.

Our answer would be:

[tex]2x*3[/tex] or [tex](2x)3[/tex]

You can assign [tex]x[/tex] a value and it will get you double the number, then triple of that number.

Sorry if it seems like I'm copying the other person.

Other Questions
Which of the following describe an angle with a vertex at E?Check all that apply. What is Modernism and how is it different from postmodernism? Can you give an example of each? Thanks!! Why must the kidnappers return the boy during the night? A) so they could not be recognizedB) to avoid being seen by the police C) to protect the privacy of the family D) to keep the neighbors from interfering 7. In a certain neighborhood of 100 families, 60 get their news from TV, 54 from the local paper, and 20 from both sources. If a family is selected at random, what is the probability that this family does not use any one of these sources for the news? Which is an ion found in a glass of water?OA. 02B. N+C. H+D. 0-SUBMIT Which of the equations below represents a line parallel to the y-axis? A. x = -y B. x = y C. x = 4y D. x = 4 According to the Declaration of Independence, what has the King of Englanddone?A. Taken away American rightsB. Refused to protect Americans from the FrenchC. Given Americans new rightsD. Protected the rights of AmericansSUBMI The ages of kids in a neighborhood are shown below. What is the mode?5,8,3,1,5, 4, 4, 6, 12, 10,4 Bill and Pete shared 1/2 of a cake. Bill got to eat twice as much cake as Pete. What fraction of the whole cake did Bill eat? Community mental help A cork weigh 2.5 gf in air. When tied to a sinker , the total weight is 20 gf in water. If the sinker alone weighs 25gf in water, find the density of the cork Which quadratic equation is equivalent to (x + 2)^2 + 5(x + 2) 6 = 0? A. (u + 2)^2 + 5(u + 2) 6 = 0 where u = (x 2) B. u^2 + 4 + 5u 6 = 0 where u = (x 2) C. u^2 + 5u 6 = 0 where u = (x + 2) D. u^2 + u 6 = 0 where u = (x + 2) (This is a question from Edg by the way) Which of the following is true for the theoretical yield of a reaction? (1 point) a It is always calculated as a ratio. b It is the yield from the excess reactant. c It is the yield from the limiting reactant. d It is always twice the value of the actual yield. what is 2n+3n +1 +8n+4 Someone have the answer please ?! A sector with a central angle measure of 4pi/5 (in radians) has a radius of 5 cm.What is the area of the sector? two types of abortion 1. what is this video illustrating about conformity?2. Why do you think the participants in the video confirmed to those around them?3. what happened during all this?Video: Everybody's Doing itplease help me..... A certain substance has a half life of 1 hour. If you start with 3000 grams of the substance, how much will you have in 1 hour? A worker pushes a wheelbarrow with a force of 20N downward and to the left, as shown in the figure below. The angle the handle makes with the horizontal is 34. Note that the figure is not drawn to scale. Write the force vector F in the form =F+aibj. Do not round any intermediate computations, and round the values in your answer to the nearest hundredth. f=