Given a geometric sequence in the table below, create the explicit formula and list any restrictions to the domain.


n an
1 −4
2 20
3 −100

an = −5(−4)n − 1 where n ≥ 1
an = −4(−5)n − 1 where n ≥ 1
an = −4(5)n − 1 where n ≥ −4
an = 5(−4)n − 1 where n ≥ −4

Answers

Answer 1

Answer:

B

Step-by-step explanation:

given the first 3 terms of the geometric sequence - 4, 20, - 100

with r = [tex]\frac{-100}{20}[/tex] = [tex]\frac{20}{-4}[/tex] = - 5

the n th term formula ( explicit formula ) is

[tex]a_{n}[/tex] = [tex]a_{1}[/tex] [tex]r^{n-1}[/tex]

here r = - 5 and [tex]a_{1}[/tex] = - 4, hence

[tex]a_{n}[/tex] = - 4 [tex](-5)^{n-1}[/tex] with n ≥ 1





Answer 2

This question is solved using geometric sequence concepts, and doing this, we get that the correct option is:

[tex]a_n = -4(-5)^{n-1}, n \geq 1[/tex], second option

Geometric sequence:

In a geometric sequence, the quotient between consecutive terms is the same, called common ration, and the general equation is given by:

[tex]a_n = a_1q^{n-1}, n \geq 1[/tex]

In which [tex]a_1[/tex] is the first term and q is the common ratio.

-------------------------------------------------------

n an

1 −4

2 20

3 −100

First term is -4, so [tex]a_1 = -4[/tex], then:

[tex]a_n = a_1q^{n-1}, n \geq 1[/tex]

[tex]a_n = -4q^{n-1}, n \geq 1[/tex]

The common ratio is:

[tex]q = \frac{-100}{20} = \frac{20}{-4} = -5[/tex]

Thus:

[tex]a_n = -4(-5)^{n-1}, n \geq 1[/tex] is the sequence.

A similar example is given at https://brainly.com/question/24078619


Related Questions

Enter the value of a and b that complete the sum: 3/x + 5/x^2 = ax+b/x^2

Answers

Answer:

a=[tex]\frac{3}{x^{2} }[/tex]

b=5

Step-by-step explanation:

we are given

[tex]\frac{3}{x} }[/tex]+[tex]\frac{5}{x^{2} }[/tex]=ax+[tex]\frac{b}{x^{2} }[/tex]

we will compare both sides of equaion

 [tex]\frac{b}{x^{2} }[/tex]=[tex]\frac{5}{x^{2} }[/tex]

comparing both sides we get

b=5

and

[tex]\frac{3}{x} }[/tex]=ax

a=[tex]\frac{3}{x^{2} }[/tex]

hence

a=[tex]\frac{3}{x^{2} }[/tex]

and   b=5

Answer:

a=3

b=5

Step-by-step explanation:

answers on edge

The sum of three consecutive odd integers is 951 What are the integers

Answers

Answer:

315, 317, and 319

Step-by-step explanation:

So first we have to set the equation up. Since it is odd, we would write

[tex](x-2)+x+(x+2)=951[/tex]

where x is the middle integer. This gets you

[tex]3x=951[/tex]

Solving for x we get

[tex]x=317[/tex]

Since x was the middle, we subtract 2 and add 2 and put them together in ascending order, or 315, 317, and 319.

Because of its conversation and easy access to ATMs ___ is the most common form of payment today.

Answers


Because of its convenience and easy access to ATMs, debit cards are the most common form of payment today. 

Debit cards are linked to your bank account and will allow you to access those available funds. If you swipe your debit card it will automatically remove funds from your bank account to pay for your items. You are also able to use it at an ATM to withdraw cash. Most debit cards have an allowed amount of money you can withdraw from an ATM in a day. 

Answer:

Step-by-step explanation:

a Debit card

apex

identify the two irrational numbers

Answers

The answers are A and B as they cannot be turned into fraction. C can be 2 7/9 and D is already a fraction so they are rational.

How do I solve this ?

Answers

Look at the picture.

ΔZYX and ΔDYC are similar. Therefore the lengths of sides are in proportion:

[tex]\dfrac{DC}{ZX}=\dfrac{DY}{ZY}[/tex]

DC = x

ZX = 16

DY = a

ZY = a + a = 2a

Substitute:

[tex]\dfrac{x}{16}=\dfrac{a}{2a}[/tex]

[tex]\dfrac{x}{16}=\dfrac{1}{2}[/tex]       multiply both sides by 16

[tex]\boxed{x=8}[/tex]

Answer: CD = 8

What are the numerical measures of the angles?


x =


m∠DEA = °


m∠AEB = °

Answers

ANSWER

The sum of m∠DEA and m∠AEB is 180°.

Reason: The sum of angles on a straight line is always 180°.

[tex](x + 25)+(9x + 10)=180 \degree[/tex]

Group like terms to get,

[tex]x+9x=180-25-10[/tex]

Simplify, and get,

[tex]10x = 145[/tex]

Divide both sides by 10 to get,

[tex]x = 14.5[/tex]

We substitute this value to get the required angles.

[tex]m \: ∠DEA=x+25[/tex]

[tex]m \: ∠DEA = 14.5 + 25 = 39.5 \degree[/tex]

[tex]m\:∠AEB=9x+ 10[/tex]

[tex]m\:∠AEB = 9(14.5) + 10 [/tex]

[tex]m\: ∠AEB=130.5 + 10 = 140.5 \degree[/tex]

Answer:

What is the numerical sum of the degree measures of ∠DEA and ∠AEB?

✔ 180

What are the numerical measures of the angles?

x =

✔ 14.5

m∠DEA =

✔ 39.5

°

m∠AEB =

✔ 140.5

°

Step-by-step explanation:

Solve the equation.
-21 = (m/3)

A) m = 7
B) m = -7
C) m = -63
D) m = 63

Answers

Answer:

C) m = -63 is your answer

Step-by-step explanation:

Isolate the variable (m). Note the equal sign, what you do to one side, you do to the other.

Multiply 3 to both sides

-21 = (m/3)

(-21)(3) = (m/3)(3)

m = (-21)(3)

Combine like terms. Simplify.

m = -21 * 3

m = -63

C) m = -63 is your answer

~

The tax on a $400 painting is $34. What shiuld be the tax on a $700 painting.

Answers

Answer:

$59.50

Step-by-step explanation:

34/400=x/700

400x=23,800

x=59.5

Answer:

see below     Please give brainliest

Step-by-step explanation:

To find the tax rate:

$34 ÷ $400 = 0.085 = 8.5%


To figure amount of tax:

$700 x .085 (8.5%) = $59.50 is the amount of tax to be paid

(3v^5+8v^3_10v^2)_(-12v^5+4v^3+14v^2)

Answers

Answer:

(3v5+8v3+10v2)+(-12v5+4v3+14v2)

Final result :

 -3v2 • (3v3 - 4v - 8)

Step by step solution :

Step  1  :

Equation at the end of step  1  :

 (((3•(v5))+(8•(v3)))+(10•(v2)))+(((0-(12•(v5)))+(4•(v3)))+(2•7v2))

Step  2  :

Equation at the end of step  2  :

 (((3•(v5))+(8•(v3)))+(10•(v2)))+(((0-(12•(v5)))+22v3)+(2•7v2))

Step  3  :

Equation at the end of step  3  :

 (((3•(v5))+(8•(v3)))+(10•(v2)))+(((0-(22•3v5))+22v3)+(2•7v2))

Step  4  :

Equation at the end of step  4  :

 (((3•(v5))+(8•(v3)))+(2•5v2))+(-12v5+4v3+14v2)

Step  5  :

Equation at the end of step  5  :

 (((3•(v5))+23v3)+(2•5v2))+(-12v5+4v3+14v2)

Step  6  :

Equation at the end of step  6  :

 ((3v5 +  23v3) +  (2•5v2)) +  (-12v5 + 4v3 + 14v2)

Step  7  :

Step  8  :

Pulling out like terms :

8.1     Pull out like factors :


  -9v5 + 12v3 + 24v2  =   -3v2 • (3v3 - 4v - 8)


Polynomial Roots Calculator :

8.2    Find roots (zeroes) of :       F(v) = 3v3 - 4v - 8

Polynomial Roots Calculator is a set of methods aimed at finding values of  v  for which   F(v)=0  


Rational Roots Test is one of the above mentioned tools. It would only find Rational Roots that is numbers  v  which can be expressed as the quotient of two integers


The Rational Root Theorem states that if a polynomial zeroes for a rational number  P/Q   then  P  is a factor of the Trailing Constant and  Q  is a factor of the Leading Coefficient


In this case, the Leading Coefficient is  3  and the Trailing Constant is  -8.


The factor(s) are:


of the Leading Coefficient :  1,3

of the Trailing Constant :  1 ,2 ,4 ,8


Let us test ....


  P    Q    P/Q    F(P/Q)     Divisor

     -1       1        -1.00        -7.00    

     -1       3        -0.33        -6.78    

     -2       1        -2.00        -24.00    

     -2       3        -0.67        -6.22    

     -4       1        -4.00        -184.00    

     -4       3        -1.33        -9.78    

     -8       1        -8.00       -1512.00    

     -8       3        -2.67        -54.22    

     1       1        1.00        -9.00    

     1       3        0.33        -9.22    

     2       1        2.00        8.00    

     2       3        0.67        -9.78    

     4       1        4.00        168.00    

     4       3        1.33        -6.22    

     8       1        8.00        1496.00    

     8       3        2.67        38.22    


Polynomial Roots Calculator found no rational roots


Final result :

 -3v2 • (3v3 - 4v - 8)


Step-by-step explanation:


Rachel decided to have bouncy balls as a party favor. She determines that her ratio of bouncy ballsTwo guest is 9:3. Explain how to find the number of balls needed for30 guest

Answers

Answer: 90


Step-by-step explanation:because  if you times 10 to get 30 so you also times it by 9 so 9 x 10 = 90


Which measures have the dotted quarter note and single eighth note so that they sound like syncopation?

Question 5 options:


Measures 1, 2, 3, and 4


Measures 2 and 4


Measures 1 and 3


Measure 2

Answers

Answer:

Measures 1 and 3

Step-by-step explanation:

Eighth notes appear as a quarter note with flag on the end. Dotted quarter notes are quarter notes with a dot.

What’s the value of x?

Answers

Answer: C: 10


Step-by-step explanation: You need to use the equation a^2+b^2=c^2. So it's 6^2+8^2=x^2.

36+64=100

Square root of 100 is 10

10^2 = 100


Mark bought a concert ticket for $88, then sold it for $121. By what percent did he mark the ticket up?

Answers

Answer:

27.27%

Step-by-step explanation:

Formula:

%= 100*(revenue-cost)/ revenue

%= 100* (121-88)/121


By 27.27%  the ticket price mark up.

What is Percentage increase?

The ratio of the increased value to the original value, multiplied by 100, is the percentage increase formula. It is outlined as a percentage. Anything's value will increase if it is valued more, so will its proportion.

Given:

Mark bought a concert ticket for $88.

Mark sold it for $121.

Change in amount= 121- 88 = $33.

So, the percent increase

= (121- 88) / 88 x 100

= 33/121 x 100

= 3/11 x 100

= 27.27%

Hence, the percent mark up is 27.27%.

Learn more about Percentage increase here:

https://brainly.com/question/27992848

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Let n be even number, then the next even number greater than n is

Answers

Answer:

If N is 38, next even number would be 40

Step-by-step explanation:

Any number ending with 0 2 4 6 8 is even, sorry if this ins't what you were asking I didn't understand completely

If two planes intersect, then they intersect in exactly one point. True or false?

Answers

Answer: False

A plane is a flat line that extends forever in all directions. Think of a flat piece of paper that does not bend or curve. If you intersect two planes, then they will form a straight line. This line will extend forever both directions. There are infinitely many points on this line of intersection. You can think of a book as a good example: the pages are the planes while the spine is the line of intersection.

12x+7<−11 OR 5x−8>40. Solve for the inequality

Answers

Final answer:

To solve the inequality 12x+7<−11 OR 5x−8>40, isolate x in each equation. The solutions are x < -1.5 and x > 9.6.

Explanation:

To solve for the inequality 12x+7<−11 OR 5x−8>40, we first need to simplify each equation separately i.e isolate x in each separate equation.

For the inequality 12x + 7 < -11: Subtract 7 from both sides, which gives 12x < -18. Then divide by 12 which will yield x < -1.5.

For the inequality 5x - 8 > 40: Add 8 to both sides, which gives 5x > 48. Then dividing both sides by 5, we get x > 9.6.

Our answer is therefore x < -1.5 OR x > 9.6. This means that any x value satisfying either of these conditions will satisfy the original inequality.

Learn more about Inequality here:

https://brainly.com/question/40505701

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To solve the compound inequality 12x + 7 < -11 OR 5x - 8 > 40, solve each inequality separately to find x < -1.5 or x > 9.6. This means x can be any value less than -1.5 or greater than 9.6.

To solve for x in the given compound inequality, we need to handle each inequality separately.

Step-by-Step Solution:

First, solve the inequality 12x + 7 < -11:Subtract 7 from both sides: 12x < -18Divide both sides by 12: x < -1.5Second, solve the inequality 5x - 8 > 40:Add 8 to both sides: 5x > 48Divide both sides by 5: x > 9.6

Therefore, the solution to the compound inequality is x < -1.5 OR x > 9.6.

This means x can be any number less than -1.5 or greater than 9.6.

14. A line that passes through the point (5,7) has a slope of 3. Which other point is on that line?

Answers

There are no answer choices, so I will just list a few. But first, we need to create the equation.

Plugging in (5,7) into the equation y=mx+b, we can solve for b since all of the other variables are known, with m=3 as the slope.

So, 7=3*5+b

7=15+b

b = -8


y=3x-8 is your equation.

So, you can plug in any value of x you get a certain value of y.

(1,-5), (2,-2), (3,1), (4,4), (5,7), (6,10), (7,13)

Answer:

(6, 10)

Step-by-step explanation:

slope = [tex]\frac{change in y}{change in x}[/tex] = [tex]\frac{3}{1}[/tex]

to find another point on the line add 3 to the y-coordinate and add 1 to the x-coordinate

(5, 7) → (5 + 1, 7 + 3) → (6, 10) ← other point on line

continue to do this for other points

(6, 10) → (6 + 1, 10 + 3) → (7, 13)



If f(x)=x^3+3x^2+4x+5 and g(x)=5x, then what is d/dx[g(f(-1))]?

Answers

Answer:

The answer is 19.4322

Step-by-step explanation:


Simplify.
1.567 + 2.345 - 1.83(5)
A) -2,082
B) -5.238
C) 2.082
D) 5.742

Answers

Hey there!

In order for you to solve this equation, you could do PEMDAS

[tex][P]arentheses[/tex][tex][E]xponents[/tex][tex][M]ultiplication[/tex][tex][D]ivision[/tex][tex][A]ddition[/tex][tex][S]ubtraction[/tex]

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

                 [tex]1.567+2.345-1.83(5)[/tex]

                [tex]1.567+2.345= 3.912[/tex]

                [tex]3.912- 1.83(5)[/tex]

               [tex]1.83(5) = 9.15[/tex]

              [tex]3.912 -9.15 = -5.238[/tex]

[tex]\boxed {AnswerB: -5,238}[/tex]

Good luck on your assignment and enjoy your day!

~[tex]LoveYourselfFirst:)[/tex]

             



Answer:

-5.238

Step-by-step explanation:

Remember your order of operations. Multiplication happens before subtraction.

3.912 - 9.15

-5.238

Outliers are always in which quartile(s) of a box and whisker plot?

A. First quartile

B. Second and third quartiles

C. First and fourth quartiles

D. Second and fourth quartiles

Answers

Answer:

C. First and fourth quartiles

Step-by-step explanation:

Let's see what outliers are.

If a data value is very far away from the quartiles (either much less than Q1 or much greater than Q3 ), it is sometimes designated an outlier .

Therefore, from the above definition.

Outliers are always in " first and fourth quartiles"

Answer: C. First and fourth quartiles.

Thank you.

what is -3/4 × -8 ?

Answers

Question

what is -3/4 × -8 ?


Answer:

6

Step-by-step explanation:

-3/4 * (-8) =

-3 * (-2) =

6



( 4 over 4 )x = 4/32 what is the value of x

Answers

4 over 4 (4/4) is equal to 1.

The equation can be rewritten as X = 4/32

4/32 can be simplified to 1/8


So you have X = 1/8

Answer:

1/8

Step-by-step explanation:

to simplify 4/32, you just have to see how many times 4 goes into 32, in this case the answer is 8. A good rule of thumb is if the smaller number is on the top of the fraction, you will get a fraction for an answer, so the 4 turns into 1 and the 32 turns into 8.

The location of four buildings are on a coordinate grid are as follows: bank at (3, −3) post office at (−2, −3) ​​ dry cleaner at (−2, 6) pizza shop at (3, 6) Liza begins at the bank and then walks to the post office, then to the dry cleaner, and then to the pizza shop. Then she walks to the bank again, where she left her cell phone. The path between each building is a straight line. One unit on the coordinate grid equals 400 yards. What is the total distance Liza walked?

Answers

Answer:

11,200 yards

Step-by-step explanation:

First, plot all the points on a graph. Then draw Liza's path. Add them all up and multiply by 400.

28 · 400 = 11,200.

Liza walked 11,200 yards.

My graph is attached. The blue line is Liza's path and each coordinate point is labeled.

I hope this helps u!!

:)


Answer:

11,200 yards.

Step-by-step explanation:

Distance between two points is;

Distance = √(x²+y²)

Distance between Bank and post office = √(5²+0)

                                                                     = 5

Distance between post office and dry cleaner = √(0+9²)

                                                                              = 9

Distance between Dry cleaner and pizza shop = √(0+5²)

                                                                                = 5

Distance between Bank and pizza shop  = √(9²-0)

                                                                    = 9

Total distance = 5+9+5+9

                       = 28 units

1 unit ⇒ 400 yards

28 units ⇒ (28×400)

              ⇒ 11,200 Units

You are going to spend &47.50 to play games at the fair. Each game costs 0.50$ per play. Which of those equations best shows how much money you have left as you play the games?

Answers

y=-.5x+47.50

47.50 is the starting amount you have
.5x is the cost per game,x, you play. the x is the number of games and .5 is the cost per game.



f(x) = -3x^2+2x-5

What is f(-1)

Answers

Answer:

- 10

Step-by-step explanation:

Wherever you see an x, put in a minus 1.

f(-1) = -3(-1)^2 + 2x - 5

f(-1) = -3(1) + 2(-1)  - 5

f(-1) = - 3 - 2 - 5

f(-1) = - 10

what is the equation of a line that has a slope of 3 and a y-intercept of -3

Answers

Answer:

y = 3x-3

Step-by-step explanation:

y = mx+b

m is your slope and b is your y-intercept

plug those numbers in

y = 3x-3

The slope-intercept form:

y = mx + b

m - slope

b - y-intercept

We have m = 3 and b = -3. Substitute:

y = 3x - 3

Which pair of rectangles is similar
A) 6,8 and 3,4
B) 6,8 and 2,4
C) 6,15 and 3,8
D) 9,15 and 3,4

Answers

If the rectangle a × b and the rectangle c × d are similar, then

a : b = c : d.

Check:

[tex]A)\ \dfrac{6}{8}=\dfrac{6:2}{8:2}=\dfrac{3}{4}\qquad\text{CORRECT}\\\\B)\ \dfrac{6}{8}=\dfrac{6:2}{8:2}=\dfrac{3}{4}\neq\dfrac{2}{4}\\\\C)\ \dfrac{6}{15}=\dfrac{6:3}{15:3}=\dfrac{2}{5}\neq\dfrac{3}{8}\\\\D)\ \dfrac{9}{15}=\dfrac{9:3}{15:3}=\dfrac{3}{5}\neq\dfrac{3}{4}[/tex]


Answer: A) 6, 8 and 3, 4.

Help ASAP! Math!! <3

Answers

Answer:

y = 13x

Step-by-step explanation:


Last week Juan worked 20.5 hours. This week he works 1.5 times as many hours as he did last. How many hours does Juan work this week?

Answers

Answer:

30.75 hours

Step-by-step explanation:

Let

x----> the number of hours worked last week

y ----> the number of hours that Juan work this week

we know that

To find out how many hours does Juan work this week, multiply the number of hours worked last week by 1.5

so

[tex]y=1.5x[/tex]

we have

x=20.5 hours

substitute

[tex]y=1.5(20.5)=30.75\ hours[/tex]

What is the length of DE

Answers

The answer is b.6, you set up a proportion of the corresponding sides in both triangles...12/9=8/x solve for x and get 6.

The length of DE is 6 inches.

I can see that from the image, DE is a horizontal line segment that is 6 units long. This is because the x-axis is labeled in units, and DE spans 6 units on the x-axis.

we know that

The triangle XYZ and DEF are similar triangles

therefore

The ratio of their corresponding sides is equal

12/8 = 9/x

x = 8 * 9/12

x = 6 Units.

Therefore the length of DE is 6 inches.

Other Questions
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