what
arithmetic sequence with a_{4}=18 and a_{10}=48

Answers

Answer 1

Answer:

[tex]a_{n}[/tex] = 5n - 2

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

given a₄ = 18 and a₁₀ = 48 , then

a₁ + 3d = 18 → (1)

a₁ + 9d = 48 → (2)

subtract (1) from (2) term by term to eliminate a₁

6d = 30 ( divide both sides by 6 )

d = 5

substitute d = 5 into (1) and solve for a₁

a₁ + 3(5) = 18

a₁ + 15 = 18 ( subtract 15 from both sides )

a₁ = 3

Then

[tex]a_{n}[/tex] = 3 + 5(n - 1) = 3 + 5n - 5 = 5n - 2


Related Questions

I don’t know if I’m right

Answers

Answer:

  A: geometric; 4 times

  B: arithmetic: 4 more

Step-by-step explanation:

An arithmetic model is a linear model, where the rate of change is constant.  Growth or decay is by a constant amount from one interval to the next.

A geometric model is an exponential model, in which the rate of change is proportional to the amount. Growth or decay is by a constant factor from one interval to the next.

__

A)

The equation for the sequence is given in "explicit" form:

  [tex]A_n=2^{2n}[/tex]

The exponent can be split so this can be rewritten as ...

  [tex]A_n=(2^2)^n=4^n[/tex]

If this were written in recursive form, it would look like ...

  [tex]A_0=1,\ A_n=4\times A_{n-1}[/tex]

The fact that terms are related by a constant factor tells you the model is geometric. The factor tells you each hour the population is 4 times what it was in the previous hour.

__

B)

The given equation is in "recursive" form. It tells you each term is 4 more than the previous one. This constant difference between terms means the model is arithmetic.

_____

Additional comment

In general, words like "more" or "increase" refer to addition, and the words "times" or "factor" refer to multiplication.

(Little tricky; worth extra points )

Which series of transformations shows that pentagon A is congruent to Pentagon B?


A. Reflect pentagon A over the y-axis, rotate it 180 degrees clockwise about the origin, and translate it 3 units up

B. Rotate pentagon A 90 degrees clockwise about the point (1,1) reflect it over the x-axis, and translate it 3 units to the left.

C. Rotate pentagon A 90 degrees clockwise about the origin, reflect it over the x- axis, and translate it 6 units to the left.

D. Reflect pentagon A over the y-axis and translate it 2 units to the left and 8 units up.

Answers

Answer:

i am pretty sure it's A or B

Step-by-step explanation:

hope this helps

→(·°ω°·)←

PLEASE ANSWER QUICKLYY IK ITS TEDIOUS CUZ THERES A LOT BUT MATH EXPERTS, HELP

Answers

Step-by-step explanation:

i answered these 3 already.

PLSS HELPP

Write down the smallest positive integer, n, such that 294n is a perfect square.​

Answers

Step-by-step explanation:

Closest square root to 294 is 17(289) + 5

294 --> 9 is 287.

289 - 287 = 2.

2 is the biggest positive integer

What is 7 / 27 as a decimal rounded to 3 decimal places?

Answers

0.259 is the answer:)

Answer:

0.259

Step-by-step explanation:

7/27 = 0.25925926

Rounded to 3 decimal places = 0.259

hope this helps!! p.s. i really need brainliest :)

You find a ring at a garage sale and purchase it for $2. Explain how you could use a simple balance and graduated cylinder to determine if it is made of gold or if it’s a fake.

Answers

Gold has a density of 19300kg/m^3 much higher than waterSo fIll the graduated cylinder with water

Density of water is 1000kg/m^3

Gold should sink downIf yes then it's pure gold

Find only C please i don't need A or B

Answers

the answer for c is (4,-5)

What is the difference between a metric and a norm?

Answers

Answer:

A norm and a metric are two different things.  .

Step-by-step explanation:

The norm is measuring the size of something, and the metric is measuring the distance between two things. A metric can be defined on any set . It is simply a function which assigns a distance (i.e. a non-negative real number) to any two elements .

The major difference between the matric and norms is that metric is a unit of measurement that measures the distance between two objects. The size of a single thing is measured by a norm.

What is measurement?

It is defined as the numerical quantity that gives an idea about an object's size, length, width, and many more. It can be used to compare two objects.

The major difference between metrics and norms is as follows:

A metric is a unit of measurement that measures the distance between two objects. The size of a single thing is measured by a norm.Metrics may be expressed on almost anything, however, a norm can only be defined on vector spaces but since the definition of a norm requires that the things measured by the norm be added and scaled.

Thus, the major difference between the matric and norms is that metric is a unit of measurement that measures the distance between two objects. The size of a single thing is measured by a norm.

Learn more about the measurements here:

brainly.com/question/4725561

#SPJ4

Please help I'll mark brainliest.

Answers

Answer:

Step-by-step explanation:

10

12

8

13

13

7

6

12

9

10

11

9        

120

Total = 120

Number of entrees = 12

Mean = 120 / 12

Mean = 10

Help to solve the equation​

Answers

Answer:

n = -1.25

Step-by-step explanation:

S(ABCD) = AB × AD

S(ABCD) = 2n × (4n + 5)

S(ABCD) = CD × AD

2n × (4n + 5) = CD × (4n + 5)

n = -1.25

PLEASE MARK ME AS BRAINLIEST AND HAVE A NICE DAY :)

Please help me no links

Answers

Answer:

F

Step-by-step explanation:

And it is the solid line because it is less than OR equal to

Dotted line would just be less than

What percent is represented by the region that is shaded?

Answers

Answer:

66 percent

Step-by-step explanation:

⅔ are shaded which is 0.6 recurring which as a percentage is 66 percent. may have to say 66.6

A movie director needs to purchase 325 films. The film has a volume of 965 in', and the density of each film is 7.6 g/in?. Each film can be purchased for $0.34 per kilogram. What is the cost of the films?

Answers

The volume of the films is the amount  of film in the case

The cost of the films is $810.41

How to determine the cost of the films?

The given paramerers are:

Volume = 965 cubic inchesDensity = 7.6 gram per cubic inches

The mass of the films is calculated as:

Mass = Density * Volume

This gives

Mass = 7.6 * 965 g

Evaluate

Mass = 7334 g

Express as kg

Mass = 7.334 kg

The unit cost is:

Unit cost =  $0.34 per kilogram

The number of films is

n = 325

So, the total cost

Total = 325 * 0.34 * 7.334

Evaluate

Total = 810.41

Hence, the cost of the films is $810.41

Read more about unit rates at:

https://brainly.com/question/26059245

5 out of 13 students will ride in a car instead of a van

Answers

Answer:

Step-by-step explanation:8

Answer:

the answer is 8 i think xddd

Please help quick!!!!!!!!!!!!!!!!!!!!

Answers

[tex]\large\sf\underline{ANSWER:}[/tex]

23.) ax²-a

a(x²-1)

a(x+1)(x-1)

24.) 2x²-5x+3

2x²-3x-2x+3

(2x²-3x)+(-2x+3)

x(2x-3)-(2x-3)

(2x-3)(x-1)

25.) xy²+8xy+15x

x(y²+8y+15)

x(y²+3y+5y+15)

x((y²+3y)+(5y+15))

x(y(y+3)+5(y+3))

x(y+3)(y+5)

#[tex]\large\sf\underline{CarryOnLearning}[/tex]

The question is below:

Answers

Answer:

D.

Step-by-step explanation:

The original antenna revolves at a rate of 30 per 2 minutes, or 15 per minute.

Twice as fast = 15 X 2 = 30 per minute

Only the data in Table D fits.

660 / 22 = 30

720 / 24 = 30

Point X is located at 11 on the number line. Point Y is 5 less than point X. Where on the number line is point Y?

Answers

Answer:

6

Step-by-step explanation:

If you draw out a number line, and a little tick for each number, X will be on the 11 mark (I'll try to do a little thing here)

1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16

The 11 is where X is

The question says that point Y is 5 LESS than point X, so we want to go down 5 numbers.

1  2  3  4  5  6  7  8  9  10  11  12  13  14  15  16f

(6 is 5 less than 11)

So the point Y will be on the 6

Pls help i will give 5 starts and brainliest question is down below 9:22

Answers

Answer:

r, p, q

Step-by-step explanation:

Answer:

#30 is 8.40   B)

#31 is R P Q  A)

Step-by-step explanation:

A line has a zero slope and passes through the point (4,-9). What is the equation of the line?
(No links please, just a simple answer)

Answers

keeping in mind that a line with a slope of "0" is a horizontal line, Check the picture below.

23 Safia says,
3, 13 and 23 are all prime numbers so
all numbers that end in 3 must be prime.
Explain why she is wrong.

Answers

Wrong because there will be sometimes a number that will be dividend by three completely.

See :-

93

93/3 = 31

63

63/3 = 21

33

33/3 = 11

[tex]\frak{\fcolorbox{black}{pink}{Black Pink in your area$~$}}[/tex]~←(>▽<)ノ

Answer:

Step-by-step explanation:

We only need to find one exception  to prove that she is wrong.

One such number is 33,  which = 3 * 11 ( noit prime).

answer fast its a test q.
based on the statement is true?

Answers

Answer:

the right answer is F (exterior angle of triangle is equal to its sum of opposite interior angle of a traingle)

Answer: W = 40 degrees.

Step-by-step explanation: When you're finding a missing interior angle, all you need is the angle measurements of the other two angles.  According to the picture, we have two 70's given, which both add up to 140.  All the interior angles of a triangle need to add up to 180, and we have 140 so far.  That's where the missing angle comes in.  When you subtract 140 from 180, you get 40, which is your missing angle.

Let me know if this is right! :)

Please help graph this inequality

Answers

Answer:

View attached graph

Step-by-step explanation:

Hope it helps!

four friends earned $5.20 for washing a car They shared the money equally how much did each friend get.

Answers

Answer:

$1.30

Step-by-step explanation:

We need to figure out how much each friend gets out of the 5.20 so we will have to divide :)

5.20/4 = $1.30

Have an amazing day!!

Please rate and mark brainliest!!!

What value of x makes this inequality true?
x - 16 < 43

Answers

Answer:

read below

Step-by-step explanation:

x - 16 < 43

there are many values that can make it true

pretty much any number that can have 16 subtracted from it and be less than 43 will work.

or any number less than or equal to 43.

for example:

34-16<43

18 < 43

3. What is the area of the triangle below? (1 point) O 6.0 ft2 O 8.6 ft2 O 15.0 ft? O 17.2 ft2 ​

Answers

Answer:

A ≈ 8.6 ft²

Step-by-step explanation:

the area (A) of the triangle is calculated as

A = [tex]\frac{1}{2}[/tex] × 7 × 3 × sin55°

  = [tex]\frac{1}{2}[/tex] × 21 × sin55°

  = 10.5 × sin55°

  ≈ 8.6 ft²( to 1 dec. place )

Theo is a cleaner,
The table shows information about the time it will take him to clean
each of four rooms in a house,
Theo wants to clean all four rooms
Room
Time
in one day
Kitchen 1 hour 50 minutes
He will have breaks for a total time
of 85 minutes,
Lounge 55 minutes
Theo is going to start cleaning at 9 am,
Bedroom 1 1/2 hours
What time will he finish cleaning?
Bathroom
35 minutes

Answers

Step-by-step explanation:

1 hour 50 minutes = 110 mins

1 1/2 hours = 90 mins

add all these:

110

90

85

55

35

when you add all these you get 375

every hour has 60 minutes

375 ÷ 60 = 6.15

if he starts at 9 am and he cleans for 6.15 hours he will be finished by 3:15pm.

Based on the number of minutes Theo will take to clean the various rooms, and the time he will take to rest, he will finish cleaning at 3:15 pm.

What time will Theo finish cleaning?

The best thing to do here is to convert all the minutes to decimals. This would make adding them up easier.

Kitchen = 1 hour 50 minutes = 1 + 50/60 = 1.833 hours

Lounge = 55 minutes = 55/60 = 0.916 hours

Bedroom = 1.5 hours

Bathroom = 35 minutes = 35/60 = 0.583

Breaks = 85 / 60 = 1.417

Add them up:
= 1.833 + 0.916 + 1.5 + 0.583 + 1.417

= 6.249 hours

= 6 + (0.249 x 60 minutes)

= 6 hours 15 minutes

The time he will finish is:

= 6 hours 15 + 9

= 1515 hours

= 3:15 pm

Find out more on operations involving time at https://brainly.com/question/1040096.

choose the name of highlighted part​

Answers

Face is the correct answer

What is the solution to the equation?
4x + 6 = 18
A. x= -6
B. x= 3
o
C. x = 6
C
D. X=
MIN

Answers

4x + 6 = 18

-6 is solution ?

4 * (-6) + 6 = 18 ?

-24 + 6 = - 18

so not the solution

3 is solution ?

4 * 3 + 6 = 18 ?

4 * 3 + 6 = 12 + 6 = 18

YES

Answer:

B. [tex]\displaystyle x = 3[/tex]

Step-by-step explanation:

[tex]\displaystyle 18 = 6 + 4x \hookrightarrow \frac{12}{4} = \frac{4x}{4} \\ \\ \boxed{3 = x}[/tex]

I am joyous to assist you at any time.

Michele's credit card had a balance of $579. 53 on August 1. On August 8, she made a payment of $500. On August 16, she made a charge of $200. On August 24, she made another charge of $350. What was her average daily balance?

Answers

By taking the average of her balance of each day of August, we will see that the average daily balance is $373.08

What was her average daily balance?

We know that:

On August 1, her balance was $579.53On August 8, her balance was $579.53 - $500 = $79.53On August 16, her balance was $79.53 + $200 = $279.53On August 24, her balance was $279.53 + $300 = $579.53

So, first, her balance is $579.53 for 7 days. Then her balance is $79.53 for 8 days, then her balance was $279.53 for another 8 days, and finally, her balance was $579.53 for the last 8 days of august.

Then over the 31 days of August, the average daily balance will be:

[tex]A = \frac{7*579.53 + 8*79.53 + 8*279.53 + 8*579.53}{31} = 373.08[/tex]

So in August, her average daily balance was $373.08

If you want to learn more about averages, you can read:

https://brainly.com/question/20118982

helppppppppppp!

do not send links.

Answers

Answer:

0.8-0.6=0.2 or 1/5, one fifth.

Step-by-step explanation:

hope this helps

Other Questions
which features of a figuer JKLM remain the same after any rigid transformation i-ready In which quadrant does lie given that sin < 0 and cos < 0? Thank You!Quadrant IQuadrant IIQuadrant IIIQuadrant IV Nike owns equipment that cost $101,900 with accumulated depreciation of $69,600. Nike asks $37,100 for the equipment but sells the equipment for $34,400. Compute the amount of gain or loss on the sale. Multiple Choice $2,100 loss. $2,700 gain. $4,800 loss. $4,800 gain. $2,100 gain. 2. According to Jung, which two archetypes work together to create a sense of wholeness, oneness, andcompletion?Hint: These archetypes are the image of the feminine in the masculine mind and the image of the masculine in the feminine mind.A. Aggression and persuasionB. Dark and lightOC. Self and othersD. Anima and animus hi i need help once again Which statement is true? A) All paragraphs are indented. B) There are extra line spaces between every paragraph. C) A good paragraph has several main ideas. D) A good paragraph usually has one main idea. It wouldn't let me say it so I'm screenshotting it. Please help!! I will give brainliest :) How many more quarters doesTommy need before he has $3.00in quarters? helpppp! need it now. The line through the points (6, 3) and (4, 5) is perpendicular to the line through which of the following points? What percentage codes for proteins, make up our bodies PUThe data set below represents the different costs of a refrigerator at a local home improvement store.$777, $498, $619. $379. $895, $1,256, $1,052b. What is the median of the second half of the data? (third quartile) 379T Help me please, thank you Omar owns a small business selling ice-cream. He knows that in the last week 32customers paid cash, 2 customers used a debit card, and 26 customers used a creditcard.aaIf next week, he is expecting 1500 customers, about how many would you expect topay with a debit card? Round your answer to the nearest whole number.a In 1994, the moose population in a park was measured to be 4180. By 1999, the population was measured again to be 3480. If the population continues to change linearly: Find a formula for the moose population, P, in terms of t, the years since 1990. P(t)=? What does your model predict the moose population to be in 2002? Match up each definition and term. Please help asap jimmy has 27 apples and there are 9 houses. he feeds the same number of apples to each horses. how many apples dose jimmy feed to each horse? HELP! PLEASE HELP RIGHT NOW!!!! I WILL CHOOSE BRAINLIEST, I PROMISE Which of the following processes requires separate plumbing? a. water reclamation b. desalination c. greywater use d. none of the above please select the best answer from the choices provided a b c d