Which recursive definition produces an arithmetic sequence where g(5) = 8 and g(10) = 10?

Which Recursive Definition Produces An Arithmetic Sequence Where G(5) = 8 And G(10) = 10?

Answers

Answer 1

Answer:

gₙ = gₙ₋₁ + 0.4, with g₁ = 6.4

Step-by-step explanation:

The n-th term of an arithmetic sequence can be written as:

gₙ = g₁ + (n - 1)*d

Where g₁ is the first value, and d is the difference between any two consecutive terms of this sequence.

Then we have the equations:

g₅ = 8 = g₁ + (5 -1)*d

g₁₀ = 10 = g₁ + (10 - 1)*d

This is a system of equations, we can rewrite this as:

8 = g₁ + 4*d

10 = g₁ + 9*d

To solve this, the first step will be isolate one of the variables in one of the equations, i will isolate g₁ in the first equation:

g₁ = 8 - 4*d

Now we can replace this in the second equation to get:

10 = 8 - 4*d + 9*d

10 = 8 + 5*d

10 - 8 = 5*d

2 = 5*d

2/5 = d = 0.4

Now with this, we can find the value of g₁ by using the equation:

g1 = 8 - 4*d = 8 - 4*(2/5) = 8 - 8/5 = 6.4

Then the nth term of this sequence can be written as:

gₙ = 6.4 + (n - 1)*0.4

This relation also can be written as:

gₙ = gₙ₋₁ + d = gₙ₋₁ + 0.4, with g₁ = 6.4

Then the correct option is the second option.


Related Questions

Jamison wants to save up his money to buy a car. His parents said they will match what he saves, up to $2000. Jamison mows lawns in the summer, and shovels snow in the winter. He charges $25 per lawn, and $20 per driveway. Let X represent the amount of money that Jamison can save so that his parents will match the amount. Let L represent the number of lawns he mows , and T represent the number of driveways he shovels. Which of the following inequalities need to be part of the system? Select all that apply.
25L + 20d < x
x (greater than or equal to) 2000
20L+25d=x
25L+20d=x
x(less that or equal to)2000

Answers

Answer:

25l+20d=x and x ≤ 2000 needs to be part of the system.

Step-by-step explanation:

Given that:

Amount charged per lawn = $25

Number of lawns = l

Amount charged per driveway = $20

Number of driveways = d

Amount saved by Jamison = x

[tex]25l+20d=x[/tex]

Amount given by parents = upto $2000

It means the parents will not give more money than $2000, therefore, we will use less than equal to inequality

x ≤ 2000

Hence,

25l+20d=x and x ≤ 2000 needs to be part of the system.

to find the quotient 3/4 by 1/8

0 multiply 4/3 by 1/8

0 multiply 3/4 by 8

0 multiply 4/3 by 8

0 multiply 3/4 by 1/8

PLZ ASAP​

Answers

Answer: D is 0.93

Step-by-step explanation:

(3/4 x 1/8 = 0.93 ) We are looking for 0.93.

4/3 x 1/8 = 0. 16

4/3 × 8 = 10.6

3/4 × 1/8 0.93

Last year, the debate club had 16 members. This year, the club has 10 members. What is the percent of change in the number of club members?

Answers

Answer:

-60%

Step-by-step explanation:

The formula for percent change is [ x2-x1/x1 ].

10-16/10

-6/10 or -0.6

~Multiply by 100%

-0.6 * 100% = -60%

Best of Luck!

Please Help
3x^2-5x+2=0

Answers

Answer: C

Step-by-step explanation:

23 x 3 =
57 + 12 =
47 + 22 =

Answers

Use a caculater shjsjsvshjsjeveujevee

Ethan sold 2/3 gallon of lemonade. Kayla sold some lemonade too. Together, they sold
1/4 gallons. Who sold more lemonade, Ethan or Kayla? How much more?

Answers

Answer:

Ethan sold more

Step-by-step explanation:

2/3 and 1/4

Simplify to 8/12 and 4/12

8/12 is more

kingston made a pot of 29 1/2c of gumbo soup. His family ate some of the gumbo for lunch. this changed the amount of the pot by -7 3/4c. then he gave some gumbo to his neighbors. This changed the amount in the pot by -6 1/2c. How many cups of gumbo are left in the pot?
please answer quickly!!!!!!!

Answers

Answer:

29 1/2-7 3/4 is 21.75

Then 21.75-1/2 is 21.25

Step-by-step explanation:

There is [tex]15\frac{1}{4}[/tex]c of gumbo soup left after Kingston's family ate and he shared some with his neighbor.

What is a fraction?

A fraction is written in the form of p/q, where q ≠ 0.

Fractions are of two types they are proper fractions in which the numerator is smaller than the denominator and improper fractions where the numerator is greater than the denominator.

Given, Kingston made a pot of [tex]29\frac{1}{2}[/tex] of gumbo soup.

His family ate some of the gumbo for lunch. this changed the amount of the pot by [tex]-7\frac{3}{4}[/tex].

So, Reaming gumbo soup is ([tex]29\frac{1}{2} - 7\frac{3}{4}[/tex]).

= (59/2 - 31/4).

= (118 - 31)/4.

= 87/4c of gumbo soup.

Then he gave some gumbo to his neighbors. This changed the amount in the pot by -6 1/2c.

= (87/4 - 13/2)c.

= (87 - 26)/4c.

= 61/4.

= [tex]15\frac{1}{4}[/tex]c of gumbo soup.

learn more about fractions here :

https://brainly.com/question/10354322

#SPJ2

Identify the angles of rotational symmetry for the figure.
+
Rotational symmetry

Answers

Answer:

144

Step-by-step explanation:

Answer:

90 180 270

Step-by-step explanation:

The dot plot show the heights of the players on two basketball teams

Answers

Answer:

Okay and? im confused there is no dot plot or question here...

Step-by-step explanation:

Answer:

H. Team B has a greater range in player heights than Team A has.

Step-by-step explanation:

just did the quiz

Find the values of a and b so that the linear system has the given solution.
Given Solution: (2, 1)
Equation 1: ax - by'= 4
Equation 2: bx - ay = 10

Answers

Answer:

a = 6, b = 8

Step-by-step explanation:

given (2,1)

2a - 1b = 4

-1a + 2b = 10

this gives us:

a + b = 14

solve for a

a = 14 - b

plug into first equations

2(14-b) - b = 4

28 - 2b - b = 4

28 - 3b = 4

24 = 3b

b = 8

now plug b back into your equation for a, and you get:

a = 14 - 8

a = 6

Find the h.c.f by division method:
399, 665, 1463.

Help!! Teachers,students,etc

Answers

16 is 69 but the answer is 83

Answer:

6 8 8 8 89 9 8 8 66 4 4 4 57 8c8 7 54

HELP PLZ
find the value of x

Answers

Answer:

x=8

Step-by-step explanation:

write the number with the least value using the digits 1 through 9. use each digit only once. explain your reasoning

Answers

Answer: 123456789

Step-by-step explanation:

We need to write a 9-digit number using the digits 1, 2, 3, 4, 5, 6, 7, 8, and 9.

(where we can use each digit only one time)

We want the value of this 9-digit to be the smallest as possible, then:

The largest single value digit (9), needs to be in the smallest value place (in the units place)

The second larger digit (8), must be in the second smallest value place (in the tens)

And so on, then the 9-digit number will be something like:

123456789

Any other permutation will be larger than this number.

Mrs. Cameron's famous peanut butter cookies call for 1 cup of peanut butter for every 1 2 of a cup of oil. Today, she wants to make a huge batch with 1 cup of oil. How much peanut butter should she use?

Answers

she would use 2 cups. please mark me brainliest. have a great day and good luck with school :)

Luis buys 6 pizza's for $36.90 at the Italian restaurant, how much does 1 pizza cost?

Answers

Answer:

$6.15 for 1 pizza.

Step-by-step explanation:

The answer is 6.15 because 36.90 divided by 6 is 6.15.

P.S Can I have brainliest?

One pizza is $6.15.

Which statement is true regarding the graphed functions?

Answers

Ducky 1 2 mini 134 delete brainly

Out of 40 students in class 8,20% were absent.How many students were present?​

Answers

Understanding:

The total number of students is 40. 8.20% of them were absent, which means the rest were present, or in other words, (100-8.20)% were present or 91.8%. We can find the actual number of present students by multiplying the percentage of present students by the total number of students.

Solution:

Present Percentage = 91.8% or [tex]\frac{91.8}{100}[/tex]

Present Students = [tex](\frac{91.8}{100})(40)=36.72[/tex], since we are dealing with people we have to round it, so the present students are actually 37.

Answer this thanks!!!!

Answers

Answer:

B

Step-by-step explanation:

$65×6%=$3.90

$3.90+$65=$68.90

m I right

PLEASE HELP ME I AM BEING TIMED I WILL GIVE YOU BRAINILIEST!!!!!!
On a road trip a family drives 350 miles per day how many days D must they travel to reach the distance of at least 1400. Solve the inequality what does the solution represent in this situation?
(Just in case you wanted to see the question I put a picture)

Answers

No. of days taken = 1400/350Ans = 4 days

Answer:

The family will travel at least 4 days.

Step-by-step explanation:

The inequality would look like this:

350d ≤ 1400

it's ≤ because the problem said that they had to travel AT LEAST a distance of 1400.

To solve the inequality, use inverse operations.

350d ÷ 350 ≤ 1400 ÷ 350

d ≤ 4

the family will travel at least 4 days.

I hope this helped and if it did I would appreciate it if you marked me Brainliest. Thank you and have a nice day!

Jada traveled 135 miles in 3 hours. Andre traveled 228 miles in 6 hours. Both Jada and Andre traveled at a constant speed.

Answers

Answer:

Jada travels faster at a speed of 45mph

Step-by-step explanation:

Jada travels faster at a speed of 45mph

When you divide the overall miles from the time it takes you get the miles per hour.

Jada: 135/3= 45

Andre: 228/6= 38

Jada travels at 45mph as Andre travels at 38mph.

Hope this helps!

Answer:

45

Step-by-step explanation:

help now fast i will mark brainlest and please don't just put the answer work it out

Answers

Answer:

a. 6276

b. 5590

c. 23128

d. 17325

e. 15090

f. 40419

g. 10496

h. 15000

i. 15648

99% sure

If I had 1 banana then I ate that banana how many of the banana would I have hint the peal First person gets brainliest

Answers

1 peal 0 banana

eeeeeeeeeeeeee

Grocery store sells tangerines in 2/5 kg bags. A customer bought 4kg of tangerines for a school party. How many bags did he buy

Answers

In order to have 4 kg, he must have 20/5 kg. Each bag is 2/5 kg, so 2/5 times 10 is 20/5 or 4kg. Therefore, he bought 10 bags of tangerines for the school party.

ARIHANNAL
Session 2: Calculator
Question 22
X+Y
Line
Guide
Jason took out an $800 loan from his bank two years ago. He recently paid $860 back to the bank. This included the original loan amount
and the simple interest charged to him.
What was the annual interest rate of Jason's loan?
a 3%
D 3.75%
7.5%
15%

Answers

Answer:

I think its 3 or 3.75 you can check

Step-by-step explanation:

I really need help on this

Answers

Answer:

i think its c i could be wrong but just go with your gut felling

Step-by-step explanation:

sam was charged $1050 in interest on a loan with a 2.5% interest rate. what was the original amount of the loan if he took 5 years to pay it back?

Answers

Answer:

$8,400=amount of loan

Step-by-step explanation:

Key:

P=Money borrowed

T=5 years (time passed)

R=0.025 (interest rate)

I=$1050 (interest charged)

Formula: I=P*R*T

Work:

1,050=P*0.025*5

1,050=P*0.125

1,050/0.125=8,400

Check

8,400*0.025*5=1,050

(thank you 7th grade math last year haha)

How do you convert a rational exponent into a radical? Use proper terminology (numerator, denominator, index, radicand, power).

Answers

Answer: 1. Well, for one they both have a 'radicand' and you can arrange both of them in a fraction form.

2. Graph is increasing, there's an asymptotic value, the domain is all real numbers, the range is y > 0. If you add a constant, you are shifting it vertically, which means it's y-intercept will change by the magnitude of the constant.

3. Linear functions are a straight line with one definite slope. Exponential functions are basically curves with their slopes, not constantly, but changing. As you increase your x-values, the linear functions lacks behind, and the exponential one becomes very large.

4. I really don't know how to explain this, it's kind of confusing.

5. You can use the slope formula: (y2-y1)/(x2-x1). Plug in values, you get:

(12-8)/(4-2). This can be simplified to 4/2 or just 2. That's his average rate of change: 2 balls per day.

6. An arithmetic sequence adds on a specific value every time. For example: {1, 3, 5, 7...}

A Geometric sequence increases every time by a common ratio. For example: {2, 6, 18, 54...}

6. If it's relative to time, then you have a parametric equation dealing with time. Just like that, you can see that 1 variable changes with respect to the other, and that implies parametricity.

Step-by-step explanation:

9514 1404 393

Answer:

  [tex]x^{a/b}=\sqrt[b]{x^a}=(\sqrt[b]{x})^a[/tex]

Step-by-step explanation:

The denominator of the fractional exponent becomes the index of the root. The exponent numerator is left as the power of the base. The exponent can be inside or outside the radical.

  [tex]x^{a/b}=\sqrt[b]{x^a}=(\sqrt[b]{x})^a[/tex]

4х + 3y = 12
х = 5y - 20


Solve the system by substitution

Answers

Answer:

y=4 and x=0

Step-by-step explanation:

4(5y-20)+3y=12

20y-80+3y=12

23y-80=12

23y=92

y=4

Substitute y as 4 to get x.

Answer:

y=4

x=0

Step-by-step explanation:

4x + 3y = 12

X - 5y =-20

Multiply second equation by 4

4x + 3y = 12

4x - 20y = - 80

Subtract

23y = 92

y = 92/23

y =4

Put the value in first equation

4x + 12 =12

So 4x = 0

Therefore x= 0

Write a linear function for each line that relates to y to x

Answers

Answer:

Please check the complete explanation below.

Step-by-step explanation:

We know that the slope-intercept form of the line equation

[tex]y = mx+b[/tex]

where m is the slope and b is the y-intercept

                                       ANALYZING TABLE 1

Part A)

Given table 1

x           0            1              2            3

y           1             3              5            7

From table 1, the y-intercept can be determined by setting  x=0 and checking the corresponding y-value.

so at x = 0, y = 1

Thus, the y-intercept is (0, 1).

From the graph, it is clear that the line W has a y-intercept (0, 1).

Therefore, table 1 represents the line W.

Part B)

Taking two points (0, 1) and (1, 3) to find the slope using the formula

m = (y₂-y₁) / (x₂-x₁)

m = 3-1 / 1-0 = 2/1 = 2

now substituting m = 2, and b = 1 in the slope-intercept form

y = mx+b

y = 2x+1

Thus, table 1 represents the line W with the equation line y = 2x+1

                                  ANALYZING TABLE 2

Part A)

Given table 2

x           0            1              2            3

y           0             3             6            9

From table 2, the y-intercept can be determined by setting  x=0 and checking the corresponding y-value.

so at x = 0, y = 0

Thus, the y-intercept (0, 0).

From the graph, it is clear that line F has a y-intercept (0, 0).

Therefore, table 2 represents the line F.

Part B)

Taking two points (0, 0) and (1, 3) to find the slope using the formula

m = (y₂-y₁) / (x₂-x₁)

m = 3-0 / 1-0 = 3/1 = 3

now substituting m = 3, and b = 0 in the slope-intercept form

y = mx+b

y = 3x+0

y = 3x

Thus, table 2 represents the line F with the equation y = 3x

                                    ANALYZING TABLE 3

Part A)

Given table 1

x           0            1              2            3

y           2             3             4            5

From table 3, the y-intercept can be determined by setting  x=0 and checking the corresponding y-value.

so at x = 0, y = 0

Thus, the y-intercept (0, 2).

From the graph, it is clear that line N has a y-intercept (0, 2).

Therefore, table 3 represents line N.

Part B)

Taking two points (0, 2) and (1, 3) to find the slope using the formula

m = (y₂-y₁) / (x₂-x₁)

m = 3-2 / 1-0 = 1/1 = 1

now substituting m = 1, and b = 2 in the slope-intercept form

y = mx+b

y = (1)x+2

y = x+2

Thus, table 2 represents the line N with the equation y = x+2

ILL GIVE BRAINLIEST IF CORRECT!! Stacey is standing in a field. She walks 11 meters west, 30 meters north, 4 meters west and finally 22 meters south. How many meters is she from her starting point?

Answers

Answer:

21 meters

Step-by-step explanation:

Answer:

17

Step-by-step explanation:

Other Questions
The Holmes Company's currently outstanding bonds have a 8% coupon and a 13% yield to maturity. Holmes believes it could issue new bonds at par that would provide a similar yield to maturity. If its marginal tax rate is 35%, what is Holmes's after-tax cost of debt? Click to review the online content. Then answer the question(s) below, using complete sentences. Scroll down to view aditionalquestionsCause and Effect Graphic OrganizersDescribe how T-charts and Star Charts can be used to organize information into cause and effect relationships.I patients are required to lay still for several hours after therapeutic angiogramtrue or false If the point (3, 10) is on f(x), which point will be on f(x)+3?please help me :( where to add the comma?This fishing pole Nathan, has seen better days. O pole, Nathan, O has, seen O Nathan O No error Mi esposo Toms y yo_____ (1)planes para ir a El Salvador. (2)_____ para la capital, San Salvador, a las 9 de lamaana. Antes de salir, (yo) (3)______ la gua turstica en mi maleta (suitcase). Despus, (4)______ las noticias en latelevisin para escuchar el pronstico (forecast) meteorolgico para la capital. En mi oficina, mi secretaria me (5)______ el itinerario con la informacin del hotel. notmxffin can u answer this please? A theater has 384 seats. Each row has 16 seats. What is the value of x in the area model? Which of the following statements is true about the role of a doctor in a patient's care?The doctor does not need to discuss a course of treatment with the patient.B.The doctor and the patient should work together to find effective treatments.The doctor is always right, so patients should do everything the physician says.DThe doctor will be very offended if a patient seeks a second opinion, so this should be avoided. The tide of the war turned with the invasion of Normandy.The invasion began on D-Day, June 6, 1944. In the earlymorning hours, thousands of troops from the United States,Canada, Britain, and France, waded ashore on fivebeaches in northern France. From there, they fought toothand nail against German forces, eventually defeating theGermans and marking the beginning of the liberation ofFrance and the end of World War II in Europe.How was the key event in this paragraph illustrated?A) with an example of the eventB) with an explanation of the eventC) with a specific statement about the eventD) with background information about the eventplzz A contracter hires 4 workers for a construction project PLZ HELP-PICTURE ATTACHEDMATHMATICS For one Chemistry test, Joan had to answer 40 questions. Of these 40 questions, Joan answered 22 of them correctly. What percent did Joan get on her Chemistry test? Round your answer to the nearest whole number if necessary. * i am confused i don't know how to solve this maybe someone on here can solve it but here is it Solve. 21r Jesse enjoys watching Rudolph the Red-Nosed Reindeer during the holidays. If Jesse watches the movie three times every year, how many times will she have seen the movie when she turns 24? Please help due at midnight!Complete the phrases.1. A mi __ __ la msica rock.2. A nosotros no __ __ comer en la cafeteria.3. A usted __ __ las pelicules de terror.4. __ __ a ud. La pelicular de terror.5. A ustedes __ __ esquiar y andar en bicicleta.6. A juan y a mi __ __ jugar al tenis.7. A Samanta y Marencia __ __ beber coca-cola.8. A daniela __ __ mucho las Fiestas!I believe the answers should include some form of "gustar" me,te,le,nos,os,les. Thank you in advance SUBSCRIBE TO DORI SMITH AND LIE THE VIDS IT IS THE ONE THAT HAS A BLUE ICON THAT HAS A D ON IT PLS DROP A SUB use of biology in health care Listen to the audio and then answer the following . Feel free to listen to the audio as many times as necessary before answering the question. What cant the student but?The answer is: C computer Which of the following can be harvested into a fuel?waterwindcoalgas