Write the first five terms of a sequence. Don’t make your sequence too simple. Write both an explicit formula and a recursive formula for a general term in the sequence. Explain in detail how you found both formulas.

Answers

Answer 1

Answer: The answer is 5, 10, 20, 40 and 80.

Step-by-step explanation: We are to write the first five terms of a sequence, along with the explicit and recursive formula for the general term of the sequence.

Let the first five terms of a sequence be 5, 10, 20, 40 and 80. These terms are taken from a geometric sequence with first term [tex]a_1 5[/tex] and common ratio [tex]r=2.[/tex]

Therefore, we have

[tex]a_2=a_1\times r,\\\\a_3=a_2\times r,\ldots[/tex]

Therefore, the recursive formula is

[tex]a_{n+1}=2a_n,~~a_1=5.[/tex]

And explicit formula is

[tex]a_n=a_1r^{n-1}.[/tex]

Answer 2

Answer:

Let the first five terms of a sequence be, 4,8,12,20,24

Ok, let me explain the meaning of term explicit and Recursive formula.

Explicit formula ,is the general formula to find any term of the sequence.

And, Recursive formula, is the method by which, we can find the nth term of the sequence if (n-1)th term of the sequence is known.

So,the explicit formula for the sequence is,

y = 4 n, where , n is any natural number.

And the recursive formula is .

y = 4 (n-1), with the help of (n-1)th term we can find nth term.

First term =4=4 × 1

Second term =8 =4 × 2

Third term =12=4×3

Fourth term =16 =4 × 4

.....................

...........................

.................................

(n-1) th term =4 × (n-1)

nth term =4 × n

Applying the simple procedure by looking at the first , second and the way the next term goes , the general and recursive formula is obtained.

As, you said you don't want simpler sequence

Consider the first five terms of the sequence, 0, 3,8,15, 24.

Explicit formula =n² + 2 n

Recursive formula=(n-1)²+2(n-1)

If,you will look at the sequence, it is neither Arithmetic nor geometric .

First term =0=0²+0×0

Second term =3=1+2=1²+2 × 1

Third term =8=4+4=2²+2×2

Fourth term =15=9+6=3²+2×3

Fifth term =24=16 +8=4²+2×4

So, Explicit formula= n²+ 2 n, where n is a whole number.

Related Questions

Julissa is running a 10-kilometer race at a constant pace. After running for 18 minutes, she completes 2 kilometers. After running for 54 minutes, she completes 6 kilometers. Her trainer writes an equation letting t, the time in minutes, represent the independent variable and k, the number of kilometers, represent the dependent variable. Which equation can be used to represent k, the number of kilometers Julissa runs in t minutes? k – 2 = 1/9(t – 18) k – 18 = 1/9(t – 2) k – 2 = 9(t – 18) k – 18 = 9(t – 2)

Answers

Answer:

the answer is C

Step-by-step explanation:

using her first part 2 kilometers in 18 minutes

total kilometers - 2

and total time - 18

so you would get:

k – 2 = (t – 18)

Which of the following is a polynomial function in factored form with zeros at 0, –3, and 4?

A. f(x) = x^3 + x^2 – 12x
B. f(x) = x(x – 3)(x + 4)
C. f(x) = x^3 – x^2 – 12x
D. f(x) = x(x + 3)(x – 4)

Answers

The answer is D.

Explanation:
You can find the zeroes of a polynomial function in factored form by setting each factor equal to zero and solve for [tex]x[/tex].

The polynomial function of answer A is not even factored, so we can rule that one out.

Lets set each one of the factors of answer B equal to zero, solve for [tex]x[/tex] and see what happens:
- [tex]x=0[/tex]
- [tex]x-3=0[/tex]
  [tex]x=3[/tex]
- [tex]x+4=0[/tex]
  [tex]x=-4[/tex]
As you can see, our zeroes are 0,3, and -4, so this is not the correct answer either.

The polynomial function of answer C is not even factored, so we can rule that one out as well.

Lets apply what we just learned to the factored polynomial of answer D:
- [tex]x=0[/tex]
- [tex]x+3=0[/tex]
  [tex]x=-3[/tex]
- [tex]x-4=0[/tex]
  [tex]x=4[/tex]
This time our zeroes are, 0, -3, and 4; therefore we can conclude that D is the correct answer.

The expression 146 ÷ 144 is equal to _____. 142 2 1410 1

Answers

1.01388888888888888888

The correct answer is 1.

To solve this problem, we need to evaluate the expression [tex]146 \div 144[/tex]and determine which of the given options it is equal to.

The calculation can be represented as:

[tex]146 \div 144 = \frac{146}{144}[/tex]

We can simplify this fraction by finding the common factor between the numerator and denominator and dividing both by that factor.

[tex]\frac{146}{144} = \frac{73 \times 2}{72 \times 2} = \frac{73}{72}[/tex]

Now, we can divide the numerator by the denominator to find the final value.

[tex]\frac{73}{72} = 1.0138\overline{8}[/tex]

Therefore, the expression [tex]146 \div 144[/tex] is approximately equal to 1.

Complete question:

The expression [tex]146 \div 144[/tex] is equal to _____.

A) [tex]142[/tex]

B) [tex]2[/tex]

C) [tex]14^{10}[/tex]

D) [tex]1[/tex]

helppppppppppppppppp

Answers

The answer is A :) 1/625

First we rewrite the expression:
(5 ^ -1) * (5 ^ -3)
Using properties of exponents we have:
(1/5) * (1 / (5 ^ 3))
Rewriting:
(1/5) * (1 / (125))
1/625
answer:
An equivalent expression is:
1/625
option 1

a flyer on a reconnaissance flight has 4 hours for a round trip. his blade can fly 200 mph in still air. he flies out from his base against a 20 mph wind and immediately returns to his base, flying with the same wind. how many hours did he take for his fight out?

Answers

When flying with the wind, the effective plane speed is 200 + 20 = 220 mph.
When flying against the wind, the effective plane speed is 200 - 10 = 180 mph.

Let d = the distance (miles) from his base to the destination.
The time (hours) to travel with the wind is
t₁ = d/220
The time (hours) to travel against the wind is
t₂ = d/180

The total time taken is 4 hours, therefore
t₁ + t₂ = 4
d/220 + d/180 = 4
d(1/220 + 1/180) = 4
0.010101d = 4
d = 396 miles

Therefore
t₁ = 396/220 = 1.8 hours = 1 hour, 48 minutes (floght in)
t₂ = 396/180 = 2.2 hours = 2 hours, 12 minutes (flight out)

Answer: 2.2 hours

PLESSSSSS HELP WILL CROWN BRAINLIEST!!!! 20PTS!!!!!!!!!!!!

Answers

We presume you want to add the two vectors.

<5, -2> + <0, 0> = ((5+0), (-2+0)> = <5, -2>

Can someone please help me

Answers

Answer:

Convert to inches to solve and then convert back. The first solution is 1 foot 10 inches.

Step-by-step explanation:

To solve convert feet inches into inches by multiplying the number of feet by 12 and adding it to the inches. Then subtract and convert back.

For example: 5 feet is 5*12=60 inches. So 5 feet 7 inches is 60+7=67.

3 feet is 3*12=36 inches. So 3 feet 9 inches is 36+9=45 inches.

Subtract the two.

67-45= 22 inches.

22 inches is 12+10. 12 inches is 1 foot. This is 1 foot 10 inches.

Solve the system of equations using the substitution method.

{2x+8y=4
x=−3y+5

Enter your answers in the boxes.

x=

y=

Answers

Answer:

Step-by-step explanation:

X=14

y=-3

Answer:

(14,-3)

Step-by-step explanation:

MATH HELP!!!
Dwight's gross semimonthly pay is $1220. To maintain his current lifestyle, how much should he save up by the time he retires?

$292800
$317200
$702720
$761280

Answers

Answer:

292,800

Step-by-step explanation:

1220*24 (24 is semimonthly)=29,280

Then you want to multiply by 10

29280*10=292,800

Dwight's save up by the time he retires will be 292800$

Dwight's gross semimonthly pay is $1220

What is the meaning of semimonthly?

semimonthly means two times per month

Semimonthly for per year is,

12(2)=24

Dwight's gross semimonthly pay is $1220.

1220*24 (24 is semimonthly)=29,280

For one year the amount will be 29280

Then you want to multiply by 10

29280*10=292,800

Therefore Dwight's save up by the time he retires will be 292800$.

To learn more about the saving visit:

https://brainly.com/question/25787382

4/5 are girls. Today 3/5 brought there lunch. What fraction of the students are girls who brought there lunch today?

Answers

4/5 * 3/5 =12/25 i think

The radius r of a circle can be written as a function of the area A with the following equation:

[tex]r= \frac{A}{ \pi } [/tex]

What is the domain of this function? Explain why it makes sense in this context.

Answers

The real formula of the radius is r = √(A/pi)

In this context, it makes sense as the radius cannot have a negative value.

Thus, the domain of the function is [0,∞)

This means that the Area can have any positive value starting from zero.

Team tool Bella gathered 15 pounds of wood in 1/3 of an hour. What was their speed in pounds per hour.

Answers

Team tool Bella gathered 15 pounds of wood in 1/3 of an hour.

1/3 of an hour is equal to 1/3 of 60 mins = 1/3 * 60 mins = 20 mins

We have to find their speed in pounds per hour( 60 mins).

Pounds of woods gathered in 1 hour or 60 mins = 15/20*60

= 15 * 3

= 45 pounds

Therefore, their speed in pounds per hour is 45 pounds / hour

Hope this helps ..!!

Thank you :)

The width of a rectangle is 6 less than twice its length. if the area of the rectangle is 110 cm^2, what is the length of the diagonal?

Answers

the answer is: 9.16485485837795, -6.16485485837795. but if you need the work here it is
Step 2. Let 2L-6 be the width since the width of a rectangle is 6 less than twice its length.

Step 3. Area A=113=L*(2L-6)

Step 4. Solving for L yields the following steps

Subtract 113 from both sides of the equation to get a quadratic equation

To solve for L, we can use the quadratic formula given as

where a=2, b=-6 and c=-113

Solved by pluggable solver: SOLVE quadratic equation with variableQuadratic equation (in our case ) has the following solutons:

For these solutions to exist, the discriminant should not be a negative number.

First, we need to compute the discriminant : .

Discriminant d=940 is greater than zero. That means that there are two solutions: .

Final answer:

The length of the rectangle is 10 cm and the width is 11 cm. Using the Pythagorean theorem, the length of the diagonal can be calculated to be √221 cm.

Explanation:

The length of the rectangle is 10 cm and the width is 11 cm.

To find the length of the diagonal, we can use the Pythagorean theorem:

Diagonal2 = Length2 + Width2

Diagonal = √(102 + 112) = √(100 + 121) = √221 cm.

The length of the rectangle is 10 cm and the width is 11 cm. Using the Pythagorean theorem, the length of the diagonal can be calculated to be √221 cm.

Factor by grouping m^2 +8mn -3mn-24n^2
20 POINTS

Answers

Group and factor the GCF, then combine (m+8n) (m-3n)

To factor this is expression, one simple way to do this is to place brackets surrounding each set of 2 terms. Do brackets around m^2 and 8mn and brackets around -3mn - 24n^2.

Then solve for the common factor in each bracket group.

m(m + 8n) - 3n(m + 8n)

(m-3n)(m + 8n) is the answer.

A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 .

What is the volume of the dilated prism?

Enter your answer, as a decimal, in the box.

Answers

First we need to find the volume of the prism without the dilated factor:

The volume would be:
Volume of the prism(without dilated) = (area of the base) * (height)
Since,
Area of base = 5[tex]ft^{2}[/tex]
Height of the prism = 10f

Volume(without dilated) = 5*10 = 50[tex]ft^{3}[/tex]

Now let us apply the dilated factor! For that you need to multiply for factor with the volume of the prism without dilation.

Volume of the dilated prism = [tex]d^{3}[/tex] * (Volume of the prism without dilation)

Where d = dilated factor. Therefore,

[tex]v = (\frac{6}{5} )^{3} * 50[/tex]

v = 86.4[tex]ft^{3}[/tex]

So the correct answer: 86.4[tex]ft^{3}[/tex]

Find (fxf)(0)

F(x)+3x-2

Answers

Final answer:

To find (fxf)(0), substitute 0 into the given function f(x) = x + 3x - 2. The resulting value is -2.

Explanation:

To find (fxf)(0), we need to substitute 0 into the given function. The function is f(x) = x + 3x - 2. Substituting 0 for x, we get f(0) = 0 + 3(0) - 2 = -2. Therefore, (fxf)(0) = f(f(0)) = f(-2).

16 POINTS. Find the x and y intercepts of number 8 show work. I think my points are wrong.

Answers

Again, I'd try graphing this thing and get your point this way. Go to Wolframalpha dot com Put
y = 2x^4 + 3x^3 - 16x - 24 into the input line.
According to wolframalpha there are 2 real roots and 2 imaginary ones.

there are places on the internet that will solve quartics for you and likely those solutions will show all 4 roots. You were right to be a little suspicious, but the question is a bit unreasonable.

Note to Moderator. Wolframalpha dot com is just a tool. the work is my own.

1. Real numbers that cannot represent as a quotient of two integers are ____ numbers.
2. The sum of a number and it’s ____ equals zero.
3. You can simplify an expression by combining it’s ____.
4. ____ is a numbers distance from zero on a number line.
5. when you make conclusions based on patterns you observe, you use ____.

Answers

1. Irrational
2. Additive inverse
3. Like terms
4. Absolute value
5. Inductive reasoning

A company need to package hazardous chemicals in special plastic rectangular prism containers that had 80 cubic feet. Find the whole number dimensions of the container that would use the least amount of plastic.

Answers

we know that
the cube is a prism rectangular with minimum surface area
then
Volume cube=b³=80-------------> b=4.31 ft

the problem is asking me for a whole number

therefore
b=4 ft------------> I assume a rectangular prism of square base
V=b²*h--------------> h=V/b²=80/4²=5 ft

the answer is 4 ft x 4 ft x 5 ft number dimensions of the container

To package hazardous chemicals in special plastic containers the dimensions of the container should be 4 × 4 × 5 feet.

A rectangular prism with a volume of 80 cubic feet needs to be designed to use the least amount of plastic. To do this, we need to find the dimensions (length, width, height) that, while maintaining the given volume, result in the minimum surface area.

The volume of a rectangular prism is given by:

Volume = length × width × height

For our case: length × width × height = 80 cubic feet

To minimize the surface area, the dimensions should be close to a cube as this shape has the smallest surface area-to-volume ratio. We will seek integer dimensions. The formula for the surface area (SA) of a rectangular prism is:

SA = 2(length × width + width × height + height × length)

We start by considering potential combinations of whole numbers whose product is 80:

1 × 1 × 801 × 2 × 401 × 4 × 201 × 5 × 161 × 8 × 102 × 2 × 202 × 4 × 102 × 5 × 84 × 4 × 5

Calculating the surface area for each configuration:

1 × 1 × 80: SA = 2(1×1 + 1×80 + 80×1) = 2(1 + 80 + 80) = 322 sq. feet1 × 2 × 40: SA = 2(1×2 + 2×40 + 40×1) = 2(2 + 80 + 40) = 244 sq. feet1 × 4 × 20: SA = 2(1×4 + 4×20 + 20×1) = 2(4 + 80 + 20) = 208 sq. feet1 × 5 × 16: SA = 2(1×5 + 5×16 + 16×1) = 2(5 + 80 + 16) = 202 sq. feet1 × 8 × 10: SA = 2(1×8 + 8×10 + 10×1) = 2(8 + 80 + 10) = 196 sq. feet2 × 2 × 20: SA = 2(2×2 + 2×20 + 20×2) = 2(4 + 40 + 40) = 168 sq. feet2 × 4 × 10: SA = 2(2×4 + 4×10 + 10×2) = 2(8 + 40 + 20) = 136 sq. feet2 × 5 × 8: SA = 2(2×5 + 5×8 + 8×2) = 2(10 + 40 + 16) = 132 sq. feet4 × 4 × 5: SA = 2(4×4 + 4×5 + 5×4) = 2(16 + 20 + 20) = 112 sq. feet

Thus, the dimensions 4 × 4 × 5 feet are the ones that use the least amount of plastic, giving a surface area of 112 sq. feet.

Find the lateral area of the square pyramid.

Answers

lateral area = 8 *4 = 32 x 22 = 704/2 = 352 square meters

If two quantities are added and the sum is zero, what do you know about the quantities?

Answers

The two values must be opposites or both 0's

Please help asap! lots of points

Answers

Hello there! I can help you! Let's start solving this by solving for the slope. In case you forgot, the formula for finding slope is y2 - y1 / x2 - x1. The points represent each values. Here's what each value would be:

y2: -5
y1: -9
x2: 10
x1: 9

Fill in the numbers for the equation and solve. -5 - (-9) is 4. 10 - 9 is 1. 4/1 is just simply 4. There. The slope is 4, but we're not done. We'll use one of the points as x and y. Point-slope form is in the form of y - y1 = m(x - x1). y1 is -9. Because that is a negative number, we will be adding, so that part is y + 9, which eliminates answer choices A and B. x1 is 9. The other part will be 4(x - 9). That eliminates answer choice C. That leaves D, with the problem in point-slope form being y + 9 = 4(x - 9). When you subtract 4x from both sides, subtract 9 to isolate the y, multiply -10 and 4 together to get -40, and subtract 5 from -40 to get -45, the equation becomes -4x + y = -45. You use the values of the second point to find the value on the x-side. There. The answer is D.

Answer:

The answer is D.

Hope I helped :)

Have a blessed day <3

~Michael~

Tim answered all the questions on his math test but got 10 answers wrong. He received 4 points for every correct answer, and there was no penalty for wrong answers. His score was 76 points.

Answers

what's the question in this it just says stuff about Tim

What metric unit would be appropriate to measure a length of two cities?

Answers

Miles or kilometers.

Two consecutive integers have a sum of 45 . find the integers.

Answers

Let one number be x

one number = x
the other number = x + 1

The sum is 45
x + x + 1 = 45
2x + 1 = 45
2x = 45 - 1
2x = 44
x = 22

x = 22
x + 1 = 22 + 1 = 23

The two numbers are 22 and 23.

Ravi is driving 440440 miles to visit his grandma. He drives at a rate of 5555 miles per hour. How many hours will it take him to get 3434 of the way there?

Answers

the correct question is
Ravi is driving 440 miles to visit his grandma. if he drives at an average rate of 55 miles per hour, how many hours will it take him to get 3/4 of the way there?

we have that
3/4 of the way--------------> (3/4)*440=330 miles

I apply a rule of three
if 55 miles----------------> 1 hour
330 miles--------------> X
X=330/55=6 hour

the answer is 6 hour

What is the common ratio of the sequence. -2,6,-18,54

Answers

The common ratio of this sequence is -3. This is evident because the 6/-2 is -3, and we know it is a sequence so the rule consistently applies.

Answer: The required common ratio of the given geometric sequence is -3.

Step-by-step explanation: We are given to find the common ratio of the following geometric sequence :

-2, 6, -18, 54, . . .

We know that

if a(n) denotes the nth term of a geometric sequence, then the common ratio is given by

[tex]r=\dfrac{a_{n+1}}{a_{n}}.[/tex]

For the given sequence, we see that

[tex]\dfrac{a(2)}{a(1)}=\dfrac{6}{-2}=-3,\\\\\\\dfrac{a(3)}{a(2)}=\dfrac{-18}{6}=-3,\\\\\\\dfrac{a(4)}{a(3)}=\dfrac{54}{-18}=-3,\\\\\vdots[/tex]

Therefore, the common ratio is given by

r = -3.

Thus, the required common ratio of the given geometric sequence is -3.

Triangle ABC is congruent to triangle XYZ. Angle A measures 50 degrees, angle B measure 2x+40 degrees, and angle Z measures 4x+8 degrees. Find the value of x.

20.5

13.67

16

10.5

Answers

angle Z is congruent to angle C, so angle C measures 4x+8
the sum of the three angles of a triangle is 180, so
50+2x+40+4x+8=180
6x++98=180
6x=82
x≈13.67

Final answer:

To find the value of x, we use the fact that the angles of a triangle sum up to 180 degrees. By setting an equation with the given angle measurements and solving for x, we find the value of x to be 13.67.

Explanation:

The student asks about determining the value of x in two congruent triangles, ABC and XYZ, given the measurements of the angles. If triangles are congruent, their corresponding angles are equal. Using the fact that the sum of the angles in a triangle is 180 degrees, and given Angle A is 50 degrees, Angle B is 2x+40 degrees, and Angle Z is 4x+8 degrees, we can set up an equation because Angle B corresponds to Angle Z in congruent triangles:

50 + (2x + 40) + (4x + 8) = 180

Combine like terms:

50 + 2x + 40 + 4x + 8 = 180

6x + 98 = 180

Subtract 98 from both sides:

6x = 82

Divide both sides by 6:

x = 13.67

Therefore, the value of x is 13.67.

help me....................

Answers

Hello there! I can help you! The first option is definitely a polynomial. It has a degree (3), a constant (value of y), and it looks like what a polynomial should. A is eliminated. B is also eliminated, because while there is no exponent, there is constand and a variable. It has a degree of 0, but it can still be called a polynomial. C has just a variable, but y is a polynomial term. It has no exponent shown, but it has no negative exponent. C is out. D is NOT a polynomial, because the squared root does not belong in a polynomial. There are no radicals or radicands allowed in a polynomial, so that expression is not a polynomial. The answer is D.

I need 21 centimeters but i need to translate that into millimeters wht is the answer in milli eters

Answers

1cm = 10mm

21cm = 10 x 21 = 210 mm

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