Which one of these formulas describes the following sequence?

1,5,12,22,35

Answers

Answer 1

We can find a formula for nth term of the given sequence as follows:

1, 5, 12, 22, 35

The 1st differences between terms:

4, 7, 10, 13

The 2nd differences :

3, 3, 3

Since it takes two rounds of differences to arrive at a constant difference between terms, the nth term will be a 2nd degree polynomial of the form: [tex]a n^2 + b n + c[/tex], where c is a constant. The coefficients a, b, and the constant c can be found.

We can form the following 3 equations with 3 unknowns a, b, c:

[tex]1 = a\cdot1^2 + b\cdot1 + c\\5 = \cdot2^2 + b\cdot2 + c\\12 = a\cdot3^2 + b\cdot3 + c[/tex]

Solving for a, b, c, we get:

a = 3/2, b = -1/2, c = 0

Therefore, the nth term of the given sequence is:

[tex]\boxed{ a_n = \dfrac{3}{2}n^2- \dfrac{1}{2} n}[/tex]


Related Questions

0.4,0.7,1.0,1.3 what is the sequence rule

Answers

Answer:

3 plus 3, that is the sequence

Logs5(3x-2) = 1 + Logs5 (x-4)

Answers

Answer:

57

Step-by-step explanation:

A jar contains 24 blue marbles 16 red marbles and 14 white marbles find the simplified ratio of total marbles to red marbles

Answers

Answer:

27:2

Step-by-step explanation:

Solve forX
9(x + 1) = 25 + x
Ox=2
Ox=3
Ox=4
Ox=5

Answers

Answer:

x=2

Step-by-step explanation:

9x+9=25+x

subtract 9 on both sides

9x=16+x

subtract x on both sides

x=2

The solution of equation 9(x + 1) = 25 + x is x =2, which is option A.

What is an equation?

An equation is a pair of algebraic equations with the equal sign (=) in the middle and the same value.

Given information:

The equation is 9(x + 1) = 25 + x.

To solve for x, we need to isolate x on one side of the equation.

9(x + 1) = 25 + x

First, we can distribute the 9:

9x + 9 = 25 + x

Next, we can simplify by subtracting x and 9 from both sides:

8x = 16

Finally, we can solve for x by dividing both sides by 8:

x = 2

Therefore, the solution is x = 2.

To learn more about the equation;

https://brainly.com/question/12788590

#SPJ7

Simplify the expression and choose the appropriate result.
3(2 + 3g)

Answers

3x2+3x3g
6+3x3g
= 6+9g

Two fair dice, one yellow and one blue, are rolled. The value of the blue die is subtracted from the value of the yellow die. Which of the following best describes the theoretical probability distribution?

Answers

Answer:

symmetric

Step-by-step explanation:

its correct.

Answer:

B symmetric

Step-by-step explanation:

It says that I need to find x for the missing angle in the equation.

Answers

Answer:

Could you possible elaborate on the question more?

Select the correct answer from each drop-down menu. The table represents function f, and the graph represents function g.



The line of symmetry for function F is _____
A.Y=9
B.X=-2
C.X=2
D.Y=9
and the line os symmetry for function G is____
A.x=1
B.y=7
C.x=-1
D.y=-7
The y-intercept of function F is____
A.less than
B.equal to
C.greater than
The y-intercept of function G.
Over the interval [2,4] the average rate of change of function F is _____
A.greater than
B.equal to
C.less than.
the average rate of change of function G.
Thank you and I'm sorry for take your time.
I appreciate you

Answers

Answer:

1) -9 (this is where the y values stop and 'go the other way')

2) 1 (this is where the y values also stop and 'go the other way')

3) greater than (the y intercept on a table is found by looking where x = 0 and seeing what y equals. on a graph its just where the line crosses the y axis)

4) less than (idrk know how to explain this one sorry)

Step-by-step explanation:

hope this helps <3

Answer:

The line of symmetry for function f is  

x = 2 and the line of symmetry for function g is x = 1

.

The y-intercept of function f is greater than

the y-intercept of function g.

Over the interval [2, 4], the average rate of change of function f is  

less than the average rate of change of function g.

Step-by-step explanation:

True or False?
The sample space is a collection of outcomes from an event?

Answers






True I hope this helped

please help with this

Answers

Answer:

[tex]S_{n}[/tex] = n² + 4n ; n = 11

Step-by-step explanation:

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [2 [tex]a_{1}[/tex] + (n - 1)d]

~~~~~~~~~

[tex]a_{1}[/tex] = 5

d = 7 - 5 = 2

[tex]S_{n}[/tex] = [tex]\frac{n}{2}[/tex] [ 2(5) + 2(n - 1)] = [tex]\frac{n}{2}[/tex] ( 8 + 2n ) = 4n + n²

[tex]S_{n}[/tex] = n² + 4n

n² + 4n = 165

n² + 4n - 165 = 0

(n + 15)(n - 11) = 0 ( n ≥ 0 ) ⇒ n = 11

please help me I'm going to fail if you don't help me​

Answers

Answer:

B

Step-by-step explanation:

Shigaraki told me

The sum of two consecutive integers is 199. Find the integers

Answers

Here’s your answer. Hope this helped!!

The two consecutive integers will be 99 and 100.

What is Algebra?

The analysis of mathematical representations is algebra, and the handling of those symbols is logic.

PEMDAS rule means for the Parenthesis, Exponent, Multiplication, Division, Addition, and Subtraction. This rule is used to solve the equation in a proper and correct manner.

The sum of two consecutive integers is 199.

Let the first number be x and the next consecutive number will be (x + 1). Then the equation will be

x + x + 1 = 199

2x = 199 - 1

2x = 198

x = 198 / 2

x = 99

Then the two consecutive integers will be 99 and 100.

More about the Algebra link is given below.

https://brainly.com/question/953809

#SPJ2

The students at Southern Junior high School are divided into four home rooms. Benjamin just moved into the school district and will be randomly assigned to one home room

Answers

Answer:

A 4 side dice.

Step-by-step explanation:

Benjamin has 4 possible homerooms with the same probability. This means that every homeroom has a 1/4 = 0.25 (or 25%) probability of getting chosen.

You could emulate this situation with a 4 sided dice (are like little pyramids) where each side of the dice would represent the selection of one of the homerooms.

If ∧ ASC ≅ ∧ KSC then ∠8 is congruent to which angle?

Answers

Answer:

B. angle 5

Step-by-step explanation:

Part C
Question
Determine the missing values in the table.
Recall that x represents the number of tickets sold and y represents the amount of money earned from ticket sales.
Type the correct answer in each box. Use numerals instead of words.
X
$20
3
6
20
$400

Answers

Answer:

40$,160$ & 60

Step-by-step explanation:

First,find the equation using y-y1/ y1-y2=x-x1=x1-x2

y-0/0-20=x-0/0-3

y=20x/3

Now put the values of x& y in the equation, for the 1st one,

y=20×6/3

=40

2nd one.y=20×24/3

=160

3rd one,

400=20x/3

X=400×3/20

=60

The values at different number of tickets and the tickets that can be bought at $400 has been determined.

What is Direct Variation?

When a variable varies directly with the other variable, i.e. on increasing one variable the other variable also increases, this relation is called Direct Variation.

Let x represent the number of tickets sold

Let y represent the amount of money earned from ticket sales.

y ∝ x

y = kx

k is the proportionality constant.

The value in the table will be used to determine the value of k,

For 3 tickets, the ticket amount is $20

20 = k * 3

k = 20/3

The relation is given by

y = (20/3) x

For 6 tickets, the value will be,

y = (20/3 ) *6 = $40

For 24 tickets the value will be,

y = (20/3) * 24 = $160

For $400, how many tickets can be bought,

400 = (20/3) * x

400*3 /20 = x

60 tickets can be bought for $400

To know more about Direct Variation

https://brainly.com/question/14254277

#SPJ5

dijkstra's algorithm

Answers

Step-by-step explanation:

Answer my question....

Bdjsdjrrnnrnnddddsnjjejjeje

Can someone help me I appreciate it

Answers

150 degrees since 180 - 30 is 150

the force of gravity depends on the distance between objects? true or false​

Answers

Answer:

True

Step-by-step explanation:

It depends on two factors :mass of the objects and distance between the objects

hope this will help u

6/8 and 24/40 are they proportional

Answers

Answer:

no they are not

Step-by-step explanation:

solve the following equation for y

x+y=3​

Answers

9514 1404 393

Answer:

  y = 3 -x

Step-by-step explanation:

Subtract x from both sides of the equation.

  x -x +y = 3 -x

  y = 3 - x

Answer:

y=3-x

explanation

its that

Evaluate. 4³ +8² = ?​

Answers

4^3+8^2
64+64
=128!

Hope that helps

Answer: 128

Work: I just did 4 to the power of 3 which is 64, and I did 8 to the power of 2 which is also 64. 64 + 64 = 128, which is the answer. I hope this helps, and stay safe. :)

Please help me with this problem​

Answers

G=10. That’s the answer hopefully u get it right

What is the solution to the equation 9(x + 2) = 27? (1 point) Group of answer choices x = 2.5 x = 0.5 x = −0.5 x = −3.5

Answers

Answer:

Well i got 1

Step-by-step explanation:

because you need to take 9*x and 9*2

9x + 18= 27

      -18    -18

9x =9 divide by 9 on each side and get one

Which system of equations has no solution?

A.
y = 7x +5
y = 7x + 5

B.
3x - 5y = 10
-3x + 5y = -10

C.
y = 3x - 2
y = 3x + 5

D.
3x - 5y = 10
-3x - 2y = 20

Answers

Answer:

A

Step-by-step explanation:

Based on a​ survey, assume that ​31% of consumers are comfortable having drones deliver their purchases. Suppose that we want to find the probability that when consumers are randomly​ selected, exactly of them are comfortable with delivery by drones. Identify the values of​ n, x,​ p, and q.

Answers

Answer:

P(X = 2) = 0.3157

Step-by-step explanation:

Let assume that the question wants us to determine the probability that, let say when 5 customers are randomly selected, exactly 2 of the customers are comfortable.

Then;

p = 0.31

n = 5; x = 2

q = 1 - p

= 1 - 0.31

= 0.69

The probability mass function is:

[tex]P(X =x) = ^n C_r * p^x *q^{n-x}[/tex]

[tex]P(X =x) = ^5 C_2 * (0.31)^2 *0.69^{5-2}[/tex]

[tex]P(X =2) = \dfrac{5!}{2!(5-2)!} * (0.31)^2 *0.69^{3}[/tex]

[tex]P(X =2) = \dfrac{5!}{2!(3)!} * (0.31)^2 *0.69^{3}[/tex]

[tex]P(X =2) = \dfrac{5*4*3!}{2!(3)!} * (0.31)^2 *0.69^{3}[/tex]

[tex]P(X =2) = \dfrac{5*4}{2!} * (0.31)^2 *0.69^{3}[/tex]

[tex]P(X =2) =10* (0.31)^2 *0.69^{3}[/tex]

P(X = 2) = 0.3157

Your payment is $375 per month for 36 months and you made a $2,500

Answers

Answer:

375 times 36

Step-by-step explanation:

375 x 36

= 35,500

35,000 - 2,500

= 11,000

Please mark this as brainlest

can someone help please​

Answers

I’d say the letter b

111.2 please help 20 points!!!!

Answers

Answer:

111.2

Step-by-step explanation:

It would just remain 111.2

The square root and the squared cancel out on eachother

For, square roots of number will be what times what gives you that number while squared numbers will give you a number multiplied by utsekf,  

HELPPPPPP I DONT GET THIS AT ALL

Answers

Answer:

1x1 and 20x32

Step-by-step explanation:

The Precision Writing Instruments Company makes two pen designs - the Cordova design and the Savannah design. These data apply, regardless of which of two pen designs is being implemented. Materials cost per pen is $6. Labor cost per pen is $5. Production overhead is
$1,000,000. Advertising and promotion is $1,000,000. Marketing research has estimated the following demand functions for the next year of sales for the two pen designs where Q represents demand in thousands and P represents price. For the Cordova design, Q = 150 - 2.5P. For the Savannah design, Q = 175 - 2.1P. A penetration strategy is proposed for the Savannah design and a price of $25 is selected. What will be the profit or loss for the first year?

Answers

9514 1404 393

Answer:

  loss of $285,000

Step-by-step explanation:

The demand for the Savannah design is estimated to be ...

  Q = 175 -2.1P = 175 -2.1(25) = 122.5 . . . . thousand pens

Then the contribution margin from sales will be ...

  122,500($25 -$6 -$5) = $1,715,000

Against a total of $2,000,000 in production and advertising costs, the net will be a loss of ...

  $2,000,000 -1,715,000 = $285,000

The first-year loss will be $285,000.

Other Questions
According to our Chapter 8 reading, the first step in time management should be Help Ill give brainliest I dont know the answer its for a grade :/ help bruh The following information is available for Fenton Manufacturing Company at June 30: Cash in bank account $ 8,455 Inventory of postage stamps $ 94 Money market fund balance $ 14,400 Petty cash balance $ 550 NSF checks from customers returned by bank $ 1,067 Postdated checks received from customers $ 891 Money orders $ 2,257 A nine-month certificate of deposit maturing on December 31 of current year $ 10,000 Based on this information, Fenton Manufacturing Company should report Cash and Cash Equivalents on June 30 of: Elephants shape their environment in many ways. They can change a forest to a grassy field or dig a hole that might become a pond. They clear large amounts of vegetation, which removes habitats for some organisms but makes the area inviting for other organisms. Which best describes possible interactions of elephants with the surroundingecosystem?A) positiveB) negativeC) neither positive nor negativeD) both positive and negative say something random cuz i already answered my own question How did the Americans have access to the west and western port cities? (give an explanation) Slope = -2/3, y-intercept = 1Write the slope-intercept form of the equation of each line given the slope and y-intercept ? n Jay's Treaty, the British pledged to stop seizing American ships. refused pay damages for seizures of American ships. promised to evacuate the chain of forts in the Old Northwest. released Americans from their pre-Revolutionary War debt obligations to British merchants. were denied most favored nation status. Please help me. I do not understand this question. PLS HELP ASAP I MISSED THIS LESSON AND THIS IS DUE AT 11:59 THANK YOU How do you convert 20x + 9y = 9 into slope intercept form? These are Theatre questions please help! (Both questions) I think 23 is correct but Im unsure and 24 I have no clue about. Will mark branilest!!! a u shaped valley is created bya, rivers.b. glaciers.c, winds. Which of the following choicescorrectly shows the way energyflows in an ecosystem?A. Seaweed to Fish to Seal to PolarBear to BacteriaB. Polar Bear to Seal to Fish toSeaweed to BacteriaC. Bacteria to Seaweed to Fish to Sealto Polar BearD. Seaweed to Bacteria to Seal to Fishto Polar Bear Who was Jose Marti? Provide two examples of how he fought against Spanish rule. Qu molculas orgnicas tienen como funcin formar parte de las membranas celulares? Technician A says that valve stem height should be checked and the top of the valve ground, if necessary. Technician B says that an incorrect valve stem height may hold the valve open. Which technician is correct The ordered pair (1, -2) is a solution to the system of linear equations.2x + y = 0-x + 2y = 5 True False Choose the best response to the following question.Cmo te llamas?Mucho gusto.Bien, gracias.Buenas tardes.Me llamo Miguel.