The sequence {an) is defined by ao = 1 and
An+1=2an +1 for n = 0,1,2,.... What is the value
of a4?

Answers

Answer 1
Answer: 31

=======================================

Work Shown:

Use the value of a0 to find the value of a1. The idea is you double the previous value, and then add 1.

[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{0+1} = 2*(a_0) + 1\\\\a_{1} = 2*(1) + 1\\\\a_{1} = 3\\\\[/tex]

Which is then used to find the value of a2. Follow the same process as before (double the previous value and then add 1).

[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{1+1} = 2*(a_1) + 1\\\\a_{2} = 2*(3) + 1\\\\a_{2} = 7\\\\[/tex]

This is used to find a3

[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{2+1} = 2*(a_2) + 1\\\\a_{3} = 2*(7) + 1\\\\a_{3} = 15\\\\[/tex]

Finally we can now find a4

[tex]a_{n+1} = 2*(a_n) + 1\\\\a_{3+1} = 2*(a_3) + 1\\\\a_{4} = 2*(15) + 1\\\\a_{4} = 31\\\\[/tex]

Recursive sequences like this aren't too bad if n is small, but as n gets larger, things become more tedious. For those cases, its best to try to find a closed form equation. If not, then the next best thing is using a spreadsheet to automate the process.


Related Questions

[tex]M\times 2^3\times 3^7=6^7.[/tex]. Find M.

Answers

Step-by-step explanation:

steps by steps are in the picture I hope this helps you!

Define the terms factor and quantity. Then for the expression −3(4+x)(z−2−y), list all of the factors, and specify which are quantities.

Answers

Answer:

A factor are numbers or variables that can be being multiplied to each other to get another number. A factor is a quantity which is used to multiply or divide another quantity to indicate a measurement difference

A quantity is the total number or amount and it is the subject in a given mathematical operation

In the expression, -3×(4 + x)×(z - 2 - y), the factors are;

-3, (4 + x), and (z - 2 - y)

The quantities are the values that are subject to the mathematical operations including;

3, 4, x, z, 2, and y

Step-by-step explanation:

The length of a rectangle is 3 times its width. The perimeter of the rectangle is 56 inches. What are the dimensions of the rectangle?

Answers

Answer:

Width=7

Length=21

Step-by-step explanation:

Width=x

length=3x

x+x+3x+3x=56

8x=56

x=7

width = x = 7

length = 3x = 21

Answer:

Length = 21 and Width = 7

Step-by-step explanation:

Length (L)= 3x width (W)

L = 3W

Perimeter (P) = 56

Perimeter = 2L + 2W

56 = 2(3W) + 2W

56 = 6W + 2W

56 = 8W

W = 56/8

W = 7

L = 3W

L = 3(7)

L = 21

therefore Length = 21 and Width = 7

which is a defind term a angle b line c point d plane​

Answers

Answer:

a angle

Step-by-step explanation:

Point, line, and plane are undefined terms.

Angle is a defined term.

simplify : -2(3v -6)

with steps too please​

Answers

Answer:

-6v - 12

v = -2

Step-by-step explanation:

Simplify:

Apply the rules of the distributed property by multiplying -2 and 3v and -2 and -6: -6v - 12

Solve:

Now that we have our simplified form, we can find what v is. First divide each side by -6 to cancel out the -6 next to v. It should now look like this: v = -2

What is f(-4) for the function f?
f(x) = 2x + 3

Answers

Answer:

[tex]\Huge \boxed{{f(-4)=-5}}[/tex]

Step-by-step explanation:

The function f(x) is given.

f(x) = 2x + 3

f(-4)

The input for the function f(x) is -4.

x is the input value.

x = -4

Replace x with -4.

f(-4) = 2(-4) + 3

Solve for the brackets.

f(-4) = -8 + 3

Evaluate.

f(-4) = -5

Answer: f(-4) = -5

Step-by-step explanation: Here we're given the function

f(x) = 2x + 3 and we're asked to find f(-4).

In other words, if we put a x into our function, we get a 2x + 3 out.

So what happens when we put a -4 into the function?

Well if we put a -4 into the function, that's f(-4), we get a 2(-4) + 3 out.

Now all we have to do is simplify on the right side.

2(-4) is -8 so we have -8 + 3 which is -5.

So f(-4) is -5.

Calculate the slope.

Answers

Answer:  2/3

Step-by-step explanation:

Since the line is going through the origin it slope will use the formula  y/x = k where k is the slope. So you can use any point on the number line to determine the slope.

use the point (3,2)  using the formula y/x = k   divide the y by x.

k = 2/3

Answer: 0.67

Step-by-step explanation:

Look at the points (3,2), (6,4), and (9,6)

simplify (5m-2n)². please help me with this.​

Answers

Answer:

25 m^2 -20mn +4n^2

Step-by-step explanation:

(5m-2n)²

(5m-2n)(5m-2n)

FOIL

first 5m*5m = 25m^2

outer 5m*-2n = -10mn

inner -2n * 5m = -10mn

last -2n * -2n = 4n^2

Add together

25m^2 -10mn -10mn + 4n^2

25 m^2 -20mn +4n^2

7. How does using a bar diagram help you in predicting the solution to ratio and rate problems?
8. How can you use a bar diagram to check the accuracy of the solution to a ratio or rate problem?
My sister need help asap​

Answers

Answer:

7) ratio and rate are actually the same thing

they gives a fixed value when two quantities when plotted on a bar diagram helps in determining as well as predicting the solution of the problem.

I'm not sure about 7

If a number line shows tick marks that are not labeled, can you determine the coordinate of a point located at an unlabeled tick mark?

Answers

If other tickmarks are labeled, then you could do some detective work (of sorts) to figure out the unlabeled tickmarks.

For example, let's say we had a number line with 1,2,3,... and let's say that 7 was covered up or erased or smudged. So we have 1,2,3,4,5,6,__,8,9. We could then easily determine that 7 must go in that blank spot. This is just one example of course.

Another example could be that if we had a tickmark right in the middle of two whole numbers, say 0 and 1. This unlabeled tickmark would most likely be 1/2 = 0.5 as its at the halfway point between 0 and 1.

if two points are givin, then exactly one line can be drawn through those two points. which geomerty trem does the statement represent

Answers

Answer:

the correct answer is

Step-by-step explanation:

hope this helps u!!

What is f(0) given f(x) = 5(x + 2)2 - 10? ​

Answers

Answer: C) 10

Work Shown:

The idea is to replace x with 0 and then use PEMDAS to simplify.

f(x) = 5(x+2)^2 - 10

f(0) = 5(0+2)^2 - 10

f(0) = 5(2)^2 - 10

f(0) = 5(4) - 10

f(0) = 20-10

f(0) = 10

Answer:

10

Step-by-step explanation:

[tex]f(x) =5(x+2)^2 -10\\\\f(0) = 5(0+2)^2 -10\\\\= 5(2)^2-10\\\\5(4)-10\\\\20-10\\\\f(0) =10[/tex]

Enter the appropriate abbreviations.

Answers

Answer:  gal / min

                 

Step-by-step explanation:

In the diagram, JOK and MON are straight lines. Angle NOP and Angle NOQ are complimentary angles. Calculate the value of x - y.

Answers

Answer:

x - y = 118

Step-by-step explanation:

Since ∠ NOP and ∠ NOQ are complimentary then ∠ POQ = 90°

Since JOK is a straight line then

∠ JOP + ∠ POQ + ∠ QOK = 180 , that is

76 + 90 + y = 180

166 + y = 180 ( subtract 166 from both sides )

y = 14

Since MON is a straight line then

∠ MOK + ∠ KOQ + ∠ QON = 180, that is

x + 14 + 34 = 180

x + 48 = 180 ( subtract 48 from both sides )

x = 132

Thus

x - y = 132 - 14 = 118

10-9/3 with an explanation

Answers

Answer:

Brainliest!

Step-by-step explanation:

you know -9/3 = -3

10-3 = 7

so the answer is 7

-9 divided by 3 is -3

10+-3=7

change to a whole or mixed 17/5

Answers

Answer:

3  2/5

Step-by-step explanation:

17/5

How many times does 5 go into 15

5*3 =15   3 times

17-15 =2  so there is 2 left over.  This goes over the denominator

3  2/5

Answer:

3 2/5

Step-by-step explanation:

[tex]17/5 = 17 \div 5 = 3\:remainder\: 2\\\\= 3\frac{2}{5}[/tex]

Daniel glues two pieces of wood together as part of a model. One piece is 1/2 inch long, and the other is 3/4 inch long. What is the total length of the wood when glued together?
5 points

Answers

Answer:

5/4

Step-by-step explanation:

Total length = Sum of the length of the two pieces of wood :

[tex] \frac{1}{2} + \frac{3}{4} \\ lcm = 4 \\ [/tex]

Adjust values according to the lcm

[tex]4 \div 2 \times 1 = 2 \\ 4 \div 4 \times 3 = 3 \\ = \frac{3 + 2}{4} \\ = \frac{5}{4} [/tex]

Answer:

(I think it MIGHT be) 5/4

Step-by-step explanation:

The girl that answered me up above is right

Hi, I'm very fonfused on what to do here.​

Answers

Answer:

C) 212.53

Step-by-step explanation:

3x60=180 (3 minutes is 180 seconds)

180+32.53=212.53 seconds

1. Which of the following is a rational number? (4 points)
V15, 116, 121, V22
O V15
O V16
O V21
O √22
Please I need help!

Answers

V16 is a rational number

The temperature at 9:00pm one evening was 40 Fahrenheit. Over the next 4 hours the temperature dropped at n average rate of 3 per hour. What was the temperature at 1:00am?

Answers

Answer:

28 degrees Fahrenheit

Step-by-step explanation:

If the temperature at 9:00pm one evening was 40 Fahrenheit. And for the next 3 hour it dropped 3 degrees per hour then it would be

40 - 4 times 3 =

40 - ( 4 times 3 ) =

40 - 12 = 28 degrees Fahrenheit

20 points!!! pls help

Answers

Answer:

C

Step-by-step explanation: c and d are not aligned unlike the rest of them.

Lee can make 18 cookies with two cups of flour. How many cookies can he make with three cups of flour?

Answers

Answer:

he can make 27 cookies.

Step-by-step explanation:

9×2 is 18

9×3 is 27

Answer:

27 cookies

Step-by-step explanation:

First find how many cookies one cup of flour can make:

18/2

9 cookies per one cup of flour.

Now find how many cookies three cups of flour can make:

9 cookies = 1 cup of flour

? = 3 cups of flour

9 × 3 = 27

Therefore:

3 cups of flour can make 27 cookies.


1) A rectangular carpet has a perimeter of 288 inches. The length of the carpet is 96 inches more than the
width. What are the dimensions of the carpet?

Answers

Answer:

The width is 24 inches and the length is 120 inches.

Step-by-step explanation:

Let x represent the width of the carpet

The length can be represented by x + 96

Create an equation:

x + x + x + 96 + x + 96 = 288

Add like terms and solve for x:

4x + 192 = 288

4x = 96

x = 24

So, the width is 24 inches. Plug this into x + 96 to find the length:

x + 96

24 + 96

= 120

So, the width is 24 inches and the length is 120 inches.

How many terms are shown? 3x-2y+4-3z

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

Answers

The answer is D i’m pretty sure but i’d get that checked out again

A medical rescue helicopter is flying at an average speed of 172 miles per hour toward its base hospital. At 2:42 p.m., the
helicopter is 80 miles from the hospital. Use this information for Items 4-5.
Which equation can be used to determine m, the number of minutes it will take the helicopter to reach the
hospital?

Answers

Answer:

The equation that can be used to determine m, the number of minutes it will take the helicopter to reach the  hospital is [tex]172 \times (\frac{m}{60} ) = 80[/tex].

Step-by-step explanation:

We are given that a medical rescue helicopter is flying at an average speed of 172 miles per hour toward its base hospital. At 2:42 p.m., the helicopter is 80 miles from the hospital.

As we know that the Distance-Speed-Time formula is given by;

                           [tex]\text{Distance} = \text{Speed}\times \text{Time}[/tex]

Here, Distance = 80 miles

          Speed = 172 miles per hour

          Time = m (the number of minutes)

Firstly, as we can see that the speed is in miles per hour but the time is in minutes, so we will convert the time in hours, i,e;

           Time = [tex]\frac{\text{m}}{60} \text{ (in hours)}[/tex]

So,  [tex]\text{Distance} = \text{Speed}\times \text{Time}[/tex]

       [tex]80 = 172 \times (\frac{\text{m}}{60})[/tex]

       [tex]\text{m} = \frac{80 \times 60}{172}[/tex]

       m = 27.91 ≈ 28 minutes.

Hence, it will take 28 minutes for the helicopter to reach the  hospital.

In right angled triangle (not drawn to scale) measurment (in cm) of two sides are indicated in figure Find value of x in case. (pic is attached on which figure is drawn)

Answers

Answer:

5.29 units

Step-by-step explanation:

By Pythagoras theorem:

[tex] {6}^{2} + {x}^{2} = {8}^{2} \\ 36 + {x}^{2} = 64 \\ {x}^{2} = 64 - 36 \\ {x}^{2} = 28 \\ x = \sqrt{28} \\ x = 5.29150262 \: units \\ x \approx 5.29 \: units[/tex]

Is there any theorem or postulate that could prove that CB and EF are congruent? it could be multiple steps but i have no idea. ill give brainliest if its right :)

Answers

Answer:

AAS (angle, angle, side)

Step-by-step explanation:

If two angles and the non-included side of one triangle are equal to the corresponding angles and side of another triangle, the triangles are congruent. The Angle Side Angle Postulate (ASA) says triangles are congruent if any two angles and their included side are equal in the triangles. An included side is the side between two angles. hope this helps you :)

Please help! Offering brainiest and 5 stars with thanks

Answers

Answer:

The answer is 21 people

Answer:

[tex]\huge\boxed{12 \ People}[/tex]

Step-by-step explanation:

According to the ranges in Histogram:

People who took 4-6 hours to finish = 12 people.

A bank charges a 14% interest per annum on a loan. What is the interest rate if charged yearly?

Answers

Answer:  Per annum means yearly so the interest rate will be 14% as well.

Step-by-step explanation:

Order the angle from smallest to larges

Answers

Answer:

BCA

Step-by-step explanation:

Answer: B, C, A

Explanation:

The smallest angle is always opposite the smallest side of a triangle. The largest angle is always opposite the largest side.  

Side AC is the shortest, so angle B is the smallest.

Side BC is the longest, so angle A is the largest

Angle C must be between angles B and A.

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