Find the 14th term of the arthmetic sequence x-1, 7x -7 , 13x-13,....

Answers

Answer 1

Since they're in arithmetic progression, there is a constant difference between consecutive terms of

[tex](7x - 7) - (x - 1) = 6x - 6[/tex]

Recursively, the sequence is given by

[tex]\begin{cases} a_1 = x-1 \\ a_n = a_{n-1} + 6x - 6 & \text{for }n\ge2\end{cases}[/tex]

By substitution, we have

[tex]a_2 = a_1 + 6x-6[/tex]

[tex]a_3 = a_2 + 6x-6 = a_1 + 2(6x-6)[/tex]

[tex]a_4 = a_3 + 6x-6 = a_1 + 3(6x-6)[/tex]

and so on, up to the 14th term

[tex]a_{14} = a_1 + 13(6x-6)[/tex]

[tex]a_{14} = (x-1) + 78 (x - 1)[/tex]

[tex]a_{17} = 79 (x - 1) = \boxed{79x-79}[/tex]


Related Questions

f) (a² - a + b)(a + b − 2)

Answers

Answer:

Step-by-step explanation:

Jasmine is 20 years old. Her brother Zac is 6 years more than half her age. Which of the following is the correct expression for Zac's age?

(20 ÷ 2) + 6

(20 ÷ 2) − 6

10 x 2 + 4

10 − (2 x 4)

Answers

(20/2) + 6
Zac would be 16 years old.

HURRY PLS!!

A company orders 22 boxed lunches from a deli for $273.90. If each boxed lunch costs the same amount, how much do 16 boxed lunches cost?

Answers

Answer:

Step-by-step explanation:

1 box costs x amount

18 boxes cos 223.20

Cross multiply

223.20 * 1 = 18 x

Divide by 18

223.20 / 18 = 18x / 18

x = 12.40

Cost of 1 box is 12.40

Answer:

It should be 199.20 for 16 boxes

Step-by-step explanation:

I divided 273.90 by 22 which came out to 12.45

so then i multiplied 12.45 by 16 and it gave me 199.20

A loaf of bread 9 in. long is cut into slices 3/8 in. thick.

Answers

Answer:

32

Step-by-step explanation:

There is nothing this but the answer is 32.

An ordinary deck of 52 cards is shuffled. what is the probability that the top four cards have (a) different denominations? (b) different suits?

Answers

The different denomination is 0.6761

The different suits are  0.1055

What are deck of cards consist of?

A standard deck of cards has four suites: hearts, clubs, spades, diamonds. Each suite has thirteen cards: ace, 2, 3, 4, 5, 6, 7, 8, 9, 10, jack, queen and king. Thus the entire deck has 52 cards total.

Given:

Deck of cards= 52

Now,

There are 4 denomination in each cards

and there are 4 suits in deck of cards

a) different denominations

=52*48*44*40/(52*51*50*49)

= 0.6761

b) different suits

=52*39*26*13/ /(52*51*50*49)

= 0.1055

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The size of a dollar bill is 6.6 cm wide, 15.6 cm long and 0.109 mm in thickness. approximately how many dollar bills are in a 0.28 inch stack.

Answers

There are 4 dollar bills are in a 0.28 inch stack.

Given that, the size of a dollar bill is width= 6.6 cm, length=15.6 cm and height= 0.109 mm= 0.109/10 =0.0109 cm.

What is the volume of the cuboid?

The volume of the cuboid is the measure of the space occupied within a cuboid. The cuboid is a three-dimensional shape that has length, breadth, and height. If we have a rectangular sheet and we go on stacking such sheets, we will end up getting a shape that has some length, breadth, and height. The formula to find the volume of the cuboid = Length × Width × Height.

Now, the volume of a dollar bill=15.6 × 6.6 × 0.0109

=1.122264 cm³

Conversion of cm³ to cubic inches.

That is, 1.122264×0.0610237=0.06848≈0.07

Now, the number of dollars bills=0.28/0.07

=4

Therefore, there are 4 dollar bills are in a 0.28 inch stack.

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What is the value of 5 x 3 + 4 y 3 when x=4 and y=3?

Answers

Answer:

96

Step-by-step explanation:

Kenny says that to find how fast Spotify is downloading songs, you can always take the number of songs left to download and divide by how long the playlist has been downloading. Do you agree or disagree? Explain.

Answers

I do not agree. To find how fast Spotify is downloading songs, divide the number of songs already downloaded by how long the playlist has been downloading.

What is division?

Division is the process of grouping a number into equal parts using another number. The sign used to denote division is ÷. Division is one of the basic mathematical operations.

For example, assume that you are downloading a playlist that has 100 songs. 80 songs have been downloaded in the past two hours. In order to determine the rate at which songs are downloaded, divide 80 by 2.

Speed = 80 / 2 = 40 songs per hour

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Please do this algebra 2 for me. Please please. You can dm in insta what you want if u solve it just to do this please

Answers

Answer:

1231938-481881388111

HELP!!!! WILL MARK BRAINLIEST!!!!
18x+3=21
Solve for x.

Answers

Answer:

x=1

Step-by-step explanation:

18x+3=21

  -3 = -3

18x= 18

18x/18 = 18/18

x= 1

Answer:

x = 1

Step-by-step explanation:

[tex]18x + 3 = 21\\18x = 21 - 3\\18x = 18\\18x/18 = 18/18\\x= 1[/tex]

33. In this code puzzle each letter has a different numerical value. The totals for each word are reached by adding together individual values. What is the total value of the word ENTREE?
tea = 30
neat = 50
tan = 40
ten = 35
tear = 55

Answers

Answer:

tear 35 is ans

pla mark me brainliest ans

Answer:

Hello,

Answer 80

Step-by-step explanation:

[tex]\left\{\begin{array}{cccc}t+e+a&=&30&(1)\\n+t+e+a&=&50&(2)\\t+a+n&=&40&(3)\\t+e+n&=&35&(4)\\t+e+a+r&=&55&(5)\end{array} \right.\\\\\\\left\{\begin{array}{cccc}n&=&20&(2)-(1)=(6)\\t+a&=&20&(7)\\t+e&=&15&(8)\\r&=&25&(5)-(1)=(9)\\t+e+a&=&30&(1)\end{array} \right.\\\\\\\left\{\begin{array}{cccc}n&=&20&(6)\\t&=&5&(7)+(8)-(1)=(10)\\a&=&15&(7)\ and \ (10)\\e&=&10&(8)\ and \ (10)\\r&=&25&(9)\\\end{array} \right.\\[/tex]

[tex]\\\\\boxed{ENTREE=3*e+n+t+r=3*10+20+5+25=80}\\[/tex]

I have a series of questions. The faster I get the answer the more point I give.

Answers

We have

28 = 2²•7

48 = 2⁴•3

and GCD(28, 42) = 2² = 4.

The table shows the amount a restaurant is donating to a local school based on various dinner bills. Is the amount of donation proportional to the dinner bill? If so, what would be the donation for a dinner bill of $50? If not, explain.

Answers

The ratio of the donation to the bill in a table from a similar question is constant, which gives;

The amount donated is proportional to the dinner bill

If the dinner bill is $50, the amount donated will be $9

How can a professional relationship between the variables be established?

The possible values in the table as obtained from a similar question are as follows;

Dinner Bill ($) Donation ($)

25 4.50

30 5.40

35 6.30

40 7.20

Let B represent the dinner bill, and let D represent the donation.

The amount of donation is proportional to the dinner bill if each corresponding value of D/B is constant.

Checking gives;

4.5/25 = 5.4/30 = 6.3/35 = 7.2/40 = 9/50

Which gives;

D/B = 9/50

D = 9/50 × B

Therefore

The amount donated is proportional to the dinner bill

If the dinner bill is $50, we have;

B = 50

Which gives;

D = 9/50 × 50 = 9

The amount donated will be, D = $9

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help. Solve for x and show work

Answers

Answer: i belive x=1

27-28=1

2x-x

x

Step-by-step explanation: hope this helps

Points on the coordinate plane
Point N is graphed on the coordinate plane.
-5-2
is
OF
Write the coordinates of point N.

Answers

If we reflect the point (-5,2) (five, -two) over the x-axis (line of symmetry) the reflected point is (-5,-2). If we reflect the point (-5,2) (five, - two) over the y-axis (line of symmetry) the reflected point is (5,2).

What are the x-axis, and y-axis?

The vertical axis is generally called the x-axis. The perpendicular axis is generally called the y- axis. The point where the x- and y- axis intersect is called the origin. The x-axis is generally the vertical axis, while the y- axis is the perpendicular axis. They're represented by two number lines that cross perpendicularly at the origin, located at( 0, 0). The x-axis is also called the abscissa and the y- axis is called the ordinate.

The point (-5,2) is plotted as red in the picture attached.

To reflect a point over the x(ax)-axis, the x(ax) value must be the same and the y value must be the opposite.

To reflect a point over the x(ax)-axis, the y(y) value must be the same and the x(ax) value must be the opposite.

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If I spend $35 every 2 weeks, how much do I spend in a year?

Answers

You would spend $910 every year. there are 52 weeks in a year and 52/2 = 26 and 26 times 35$ is 910$

Find the center of mass of the wire that lies along the curve r and has density =4(1 sin4tcos4t)

Answers

The mass of the wire is found to be 40π√2 units.

How to find the mass?

To calculate the mass of the wire which runs along the curve r ( t ) with the density function δ=5.

The general formula is,

Mass = [tex]\int_a^b \delta\left|r^{\prime}(t)\right| d t[/tex]

To find, we must differentiate this same given curve r ( t ) with respect to t to estimate |r'(t)|.

The given integration limits in this case are a = 0, b = 2π.

Now, as per the question;

The equation of the curve is given as;

r(t) = (4cost)i + (4sint)j + 4tk

Now, differentiate this same given curve r ( t ) with respect to t.

[tex]\begin{aligned}\left|r^{\prime}(t)\right| &=\sqrt{(-4 \sin t)^2+(4 \cos t)^2+4^2} \\&=\sqrt{16 \sin ^2 t+16 \cos ^2 t+16} \\&=\sqrt{16\left(\sin t^2+\cos ^2 t\right)+16}\end{aligned}[/tex]

Further simplifying;

[tex]\begin{aligned}&=\sqrt{16(1)+16} \\&=\sqrt{16+16} \\&=\sqrt{32} \\\left|r^{\prime}(t)\right| &=4 \sqrt{2}\end{aligned}[/tex]

Now, use integration to find the mass of the wire;

       [tex]\begin{aligned}&=\int_a^b \delta\left|r^{\prime}(t)\right| d t \\&=\int_0^{2 \pi} 54 \sqrt{2} d t \\&=20 \sqrt{2} \int_0^{2 \pi} d t \\&=20 \sqrt{2}[t]_0^{2 \pi} \\&=20 \sqrt{2}[2 \pi-0] \\&=40 \pi \sqrt{2}\end{aligned}[/tex]

Therefore, the mass of the wire is estimated as 40π√2 units.

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The complete question is-

Find the mass of the wire that lies along the curve r and has density δ.

r(t) = (4cost)i + (4sint)j + 4tk, 0≤t≤2π; δ=5


Evaluate the expression for the given values of the variables.
-k²-(4k - 7n) + 3n; k= -2 and n=-5
For k = -2 and n=-5, -k²-(4k-7n) + 3n=
(Simplify your answer.)

Answers

the answer for given expression is 54

How do you define expression in math?

An expression in math is a sentence with a minimum of two numbers or variables and at least one math operation. This math operation can be addition, subtraction, multiplication, or division.

An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An equation is made up of two expressions connected by an equal sign.

the given expression is

[tex]-k^2 - (4k-7n)+3n\\-k^2 -4k +7n+3n\\put k = -2 and n=5\\-( -2)^2 - 4(-2) + 10 *5\\-4 +8+50\\54the answer for given expression is 54[/tex]

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Choose the correct scientific notation.1,345,080,000

Answers

The scientific notation form of the given number 1,345,080,000 is 1.34508 × 10⁹.

What is the scientific notation form?

Given the number in the question;

1,345,080,000

To convert to scientific notation;

First, move the decimal so there is one non-zero digit to the left of the decimal point.

Now, the number of decimal places you move will be the exponent on the 10

Note that; if the decimal is being moved to the right, the exponent will be negative, also, If the decimal is being moved to the left, the exponent will be positive.

1.345080000

We moved 9 decimal places to the left

1.34508 × 10⁹

Therefore the scientific notation form of the given number 1,345,080,000 is 1.34508 × 10⁹.

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Wyatt made a scale drawing of a picnic area near the river. The picnic area, which is 84 yards
long in real life, is 231 inches long in the drawing. What scale did Wyatt use?
11 inches : ? yards

Answers

The scale used by Wyatt is; 11 inches : 4 yards.

What is defined by the term scale factor?The Scale Factor is utilised to scale forms in various dimensions. The scale factor is a measurement for figures with similar appearances but distinct scales or measures. Assume two circles appear similar but have different radii.The scale factor specifies how much larger or smaller a figure is than the earlier figure.

Now, for the given values in question.

For the area of picnic is 84 yards.= long.

The length in the drawing is 31 inches.

Let the scale for yards is 'x'.

Then;

231 inches: 84 yards = 11 inches: x yards

Write in the fraction form,

231/84= 11/x

Cross multiplying;

x = (11×84)/231

x = 4

Thus, scale becomes; 11 inches : 4 yards.

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translate the following statement into an equation and solve for x: the number 80 is the product of "-10" and x

Answers

The value of x is -8 in the equation.

How to calculate the equation?

It should be noted that the information is that the number 80 is the product of "-10" and x.

This will be represented as:

-10 × x = 80

-10x = 80

Divide both side by -10

-10x/-10 = 80/-10

x = -8

Therefore, the value of x is -8.

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2173 rounded to neatest hundred

Answers

Answer:

2200

Step-by-step explanation:

that is the answer jf

please help quick im so confused

Answers

Answer:

(-5/2,-4)

Step-by-step explanation:

the answer is (x, y) = (-5/2, -4)

22 17 25 41 39 4
Work out the difference between the two prime numbers in the list above.

Answers

The difference between the two prime numbers 17 and 39 is 22.

What are referred as the prime numbers?

Prime numbers are those who have only two factors: 1 and the number on its own.

A prime number is a number greater than one with precisely two factors, i.e., 1 as well as the number itself. For example, the number 7 has only two factors: 1 and 7. As a result, it is a prime number. However, the number 6 has four factors: 1, 2, 3, and 6. It is a composite numbers.A prime number is one that is the whole number larger than one.It has only two factors: 1 and the number it's own.There's only the one even prime number: 2.Such a two prime numbers always are co-prime numbers.Every number can be represented as a prime number product.

For the number given:

22 17 25 41 39 4

The two primes numbers are 17 and 39.

The difference is 39 - 17 = 22.

Thus, the difference between the two prime numbers is 22.

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Aliya hikes up a mountain for 2 hours. During this time, she hikes a
distance of 1 miles. Which expression shows Aliya's rate in miles per
1
hour?

Answers

The expression shows Aliya's rate in miles per hour will be 1/2.

How to compute the expression?

From the information, Aliya hikes up a mountain for 2 hours and during this time, she hikes a distance of 1 miles.

Therefore, the rate will be:

= Distance / Time

= 1 / 2

Therefore, the expression shows Aliya's rate in miles per hour will be 1/2.

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Given j(-8,-5) and l(6,-11) if k(r-4,2s) is the midpoint of jl which correctly gives the values of r and s?

Answers

The values of r and s is -1 and -4 respectively.

Given that:-

coordinates of j are (-8,-5)

coordinates of l are (6,-11)

coordinates of k are (r-4,2s)

Also, k is the mid-point of jl.

We have to find the values of r and s.

We know that, for  (x,y) and (z,w), the mid-point is ((x+z)/2, (y+w)/2).

Here,

(x,y) = (-8.-5)

(z,w) = (6,-11)

(r-4,2s) = ((x+z)/2,(y+w)/2)

Hence,

(r-4,2s) = ((-8+6)/2,(-5-11)/2)

(r-4,2s) = (-1,-8)

Comparing the coordinates, we get:-

r - 4 = -1

r = -1+4 =3

2s = -8

s =-8/2 = -4

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How do you make the number 38 with 3,4,2,7

Answers

Answer:

2*7*3-4

Step-by-step explanation:

It think it works? 14*3 is 42-4 is 38

HELP PLS EXPLAIN THISSSS
(image included)

Answers

Answer:

The slope is [tex]-\frac{3}{4}[/tex]

Step-by-step explanation:

To find the slope, you take 2 points and use rise/run. I used (0,1) and (4,-2) because they look like they are being touched by the line. So by looking at the graph, I have to look at how I can get from (0,1) to (4,-2). So from (0,1), I go down 3 units which makes my number -3, over the run which is 4 units to the right, which makes it positive. so I went down 3 and then went right 4, making this    [tex]-\frac{3}{4}[/tex]. You could also use point-slope which means [tex]\frac{y2-y1}{x2-x1}[/tex] or [tex]\frac{-2-1}{4-0}[/tex] which equals the same thing

Write a declaration for a variable rate_of_pay that can hold values like 11.50 or 12.75.

Answers

Float rate_of_pay  a declaration for a variable rate_of_pay that can hold values like 11.50 or 12.75.

What is   float rate_of_pay?

In contrast to fixed (or unchangeable) interest rates, floating interest rates change on a regular basis. Companies that offer credit cards and mortgages frequently use floating rates. Floating rates follow the market, a benchmark interest rate, an index, or both.

Is a fixed or floating rate preferable?

In a rising rate environment, banks offer fixed rate loans at a higher rate than variable rate loans in order to profit more from the latter when rates rise. Fixed rate loans may have interest rates that are 300–350 basis points higher than floating rate loans.

float rate_of_pay

rate_of_pay = 11.50, 12.75;

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Which of the following is equivalent to the expression x² - 64?
A) (x-8)²
B) (x-64)²
C)(x-8)(x-8)
D) (x+8) (x-8)

Answers

D (x+8) (X-8)
Hope this helps
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