A sequence is defined recursively as follows: a(1) = 1, and a(n)= a(n-1)+n
(a) How do you interpret this recursive rule?

b) Write down the rule for a(2),a(3), and a(4)
it down in your own words.
and determine their values.

Answers

Answer 1

Answer:

Step-by-step explanation:

a) The current term number is added to the previous term to get the current term.

__

b) Using n = 2, 3, 4 in the given formula, we have ...

  a2 = a1 +2 = 1 +2 = 3

  a3 = a2 +3 = 3 +3 = 6

  a4 = a3 +4 = 6 +4 = 10

The value of the current term is the sum of all positive integers up to the term number, that is, term n is the n-th "triangle number."


Related Questions

Distributive property to remove parentheses 4(3+w)

Answers

Answer:

12+4w

Step-by-step explanation:

Multiply 4 by both sides

- Draw A' the symmetric of A with respect to point O

- Draw A' the symmetric of A with respect to (d) ​

Answers

Answer:

how am i supposed to answer this? draw a line lol

Step-by-step explanation:

Evaluate the expression 5xy+ -2xy+y^2 when x=4 and y=-5

Answers

Answer:

Hope it will help you...

whats 3y/2 if y = -2​

Answers

Answer:

-3

Step-by-step explanation:

3(-2)/2

-6/2 = -3

Pls help I’ll brainlest ASAP

Answers

To find the slope, you divide the difference of the y-coordinates of 2 points on a line by the difference of the x-coordinates of those same 2 points.
2 / 3 = 0.7 i think

MODELING REAL LIFE A charm bracelet costs $65, plus $25 for each charm. The equation -25x+y=65 represents the cost y (in dollars) of the bracelet, where x is the number of charms.

a. Graph the equation.

b. How much does a bracelet with three charms cost?

Answers

Answer:

B = $140

Step-by-step explanation:

for part A, the graph is linear line with a Y intercept at (0,65) so this means that if you were to have no charms it would cost 65 dollars, since the y axis represents cost. then for every 1 increment on the x axis (number of charms) the Y value increases by 25 so the slope is [tex]\frac{25}{1}[/tex]

we also can conclude that there is no negative domain since you cannot have negative charms, and the range begins at 65 since you cannot get a bracelet for less money

for part B, y=25x+65

so for three charms, x is represented as 3 so y=25(3) +65 which is 75+65=y= $140

The owner of a local shop made a list of how much she pays her employees by the hour.




Which measure of central tendency would the store owner use if she wanted to argue that the employees are paid well?

A. the mean
B. the median
C. the mode
D. the range
GIVING BRAINLIST

Answers

Answer: The answer is D

Step-by-step explanation:

I took the quiz

What is the slope of this line?


a.−23

b.−13

c.13

d.23

Answers

Answer:

D

Step-by-step explanation:

I think you meant to put the answers as a fraction

Answer:

if there were slashes in between every answer, the answer would be

D. 2/3

Step-by-step explanation:

m = y2-y1 / x2-x1  (slope formula)   ⋅the two points i used were: (0,-3) and (3,-1)

m = -1-(-3) / 3-0 (plug in the points)

m = -1+3 / 3-0

m = 2/3 (Simplify to get your answer)

During a 12-hour car ride, each of 4 family members gets to choose the music for an equal amount of time. Write an equation, where t is time, to find out how long each member of the family is in charge of selecting the music.

Answers

t=12/4
If you need to split it equally just divide the whole by the amount of parts you need

The variables x and y are directly
related. When x=15, y = 6. What is the
value of x when y = -4?

Answers

Answer: When y = -4, x = -10.

Explanation:
The equation for direct variation is y = kx^n, where k is the constant of variation. n is the exponent above the x value, but since this problem doesn’t involve exponents greater than one, we can ignore it.

First, find k.
y = kx
6 = k*15
k = 6/15 or 2/5

Now, we can solve for any x or y input. Let’s find x when y = -4.
y = kx
-4 = 2/5 * x
(to cancel out the fraction, multiply each side of the equation by its reciprocal, 5/2)
x = -4 * 5/2
x = -20/2
x = -10

what is the value of 7​

Answers

7 can be written as :-

7 + 0 = 7

7 - 0 = 7

7 × 1 = 7

7 ÷ 1 = 7

7¹ = 7

_____

Hope it helps ⚜

Solve the following system of equations.

x - 2y = -2
7x - 3y = 19

Answers

Answer:

Step-by-step explanation:

x-2y=-2     x=2y-2

7x-3y=19

substitute x  with 2y-2

7(2y-2)-3y=19     14y-14-3y=19       11y=33   y=3

substitue 3 for y

x-2(3)=-2     x-6=-2      x=4

x=4, y=3

btw if theres more similar questions like this use symbolab a website that solves and show you step by step in solving equations

really useful

The Hu family goes out for lunch, and the price of the meal is $52. The sales tax on the meal is 6%, and the family also leaves a 20% tip on the pre-tax amount. What is the total cost of the meal?

Answers

Answer:

$65.52

Step-by-step explanation:

52 x 6% = 3.12. Multiply the price of the meal by the percentage of sales tax

52 x 20% = 10.4. Multiply the price of the meal by tip percent

$3.12 is the sales tax on the meal

$10.40 is the tip amount

$52 + $3.12 + $10.40 = $65.52

Add sales tax and the tip amount to the price of the meal to find the total

Which expressions represents "2 less than the product of 5 and a number"?
A) 5n - 2
B) 5/n - 2
C) 2 - 5n
D) 5 + n - 2

Answers

Answer:

Option A is correct.

Step-by-step explanation:

Let's read the part of the question carefully.

(2 less than the product of 5 and a number)

The phrase "2 less" means subtracting 2 from the minuend."the product of 5 and a number" means multiplication of 5 and a number (5x)

Conclusion:

Therefore:

Our expression is 5n - 2

Hoped this helped.

[tex]GeniusUser[/tex]

Graph question
f(x)=3/5x-5
two points of function

Answers

Step-by-step explanation:

1) plot a point at (0,-5)

2) count 3 units up and 5 units to the right, plot the new point

3) connect the points with a straight line

4x+4 =
What is the answer to this please help

Answers

Answer:4(x+1)

Step-by-step explanation:

4x+1

If there are 10,000 people on a space ship and 7.5 potatoes grow out of 1 potato plant. How many potato plants are we going to need per person?

Answers

This can be answered by the equation 10,000 / 7.5 = 1,333.33, so we can round to 1,333.

Hope this helps!

Answer: 1333

Step-by-step explanation:

A bakery sells two kinds of baked goods: cookies and pie slices. A cookie costs 12 ani a pe sites $4. In one day, the store sold 34 baked goods for a total of $114. How many cookies die itey sele? How many pie slices did they sell? Write a system of equations and solve.​

Answers

Answer:

uhhhhhhhhhhhh what does this say?

Solve for g. Make sure to use scrap paper to show your work.

( 144 + 6 x 8 ) ÷ 3 = g

192
64
48
NO NOT PUT THIS IN A FILE

Answers

Answer:

64

Step-by-step explanation:

P E D M A S

() ² ÷ × + -

6 x 8 = 48

114 + 48 = 192

(192) ÷ 3 = g

192 / 3 = 64

g = 64

The table below shows the cumulative distance and the number of hours Ryan drove on vacation.

Hours Driving Distance Traveled (miles)
0 0
3 186
4 248
7 434
10 620

Based on the information in the table, at what speed did he drive (miles per hour)?
A.
69 miles per hour
B.
62 miles per hour
C.
52 miles per hour
D.
42 miles per hour

Answers

Answer: 62 miles per hour

Step-by-step explanation:

620/10 = 62

The speed of Ryan is given by the slope m = 62 miles per hour

What is an Equation of a line?

The equation of a line is expressed as y = mx + b where m is the slope and b is the y-intercept

And y - y₁ = m ( x - x₁ )

y = y-coordinate of second point

y₁ = y-coordinate of point one

m = slope

x = x-coordinate of second point

x₁ = x-coordinate of point one

The slope m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Given data ,

Let the equation of line be represented as A

Now , the value of A is

Let the first point be P ( 3 , 186 )

Let the second point be Q ( 4 , 248 )

Now , the slope of the line is m = ( y₂ - y₁ ) / ( x₂ - x₁ )

Substituting the values in the equation , we get

Slope m = ( 248 - 186 ) / ( 4 - 3 )

m = 62 miles per hour

Hence , the rate of change of speed is m = 62 miles per hour

To learn more about equation of line click :

https://brainly.com/question/14200719

#SPJ2

Does a quadratic polynomial have a degree of to

Answers

Answer:

Idioet duh it does.

Step-by-step explanation:

Which of the following equations has no solution?
3x + 1 = 3x + 1
3x+1= 3x + 2
3x+1= 2x + 1​

Answers

Answer:

3x+1=3x+1

0x=0

no solution

3x+1=3x+2

0×=1

no solution

3x+1=2x+1

x=0

X IS THE SOLUTION BTW

Pre college need withh

Answers

Answer:

Step-by-step explanation:

f(9) = |9 + 9| = |18| = 18

f(-4) = |-4 + 9| = |5| = 5

f(0) = |0 + 9| = |9| = 9

pretty boring examples as you're always taking the absolute value of a positive number.

what do you suppose f(-12) is???

f(-12) = |-12 + 9| = |-3| = 3

For an experiment, the temperature of a liquid must stay above 60.5°F. The starting temperature of the liquid is 88.6°F. It is placed in a cooler, which lowers its temperature 2°F each minute.

How many minutes can the liquid can stay in the cooler?

Select from the drop-down menus to correctly complete the statement. at least 14.05 /more than 14.05/ fewer than 14.05 /at most

Answers

14.05 at most

If it is saying at least, than it would be in the cooler for longer than it should be and drop below 60.5

If saying more than 14.05, it is basically the same thing where it is inside the cooler for longer than it should be

If saying at most, that means that 14.05 is the max it would be in the cooler and keeps the liquid above 60.5

Answer: im late but here you go

12/2/22

Step-by-step explanation:

Two angles are complementary. The larger angle is 32° larger than the smaller angle. Find the measure of both angles, and separate your answers with a comma.​

Answers

The angles are 29° and 61°.

Let the smaller angle be x

Let the larger angle be x+32.

The sum of the complimentary angles will be 90°.

Therefore, x + x + 32° = 90°

2x + 32° = 90°

2x = 90° - 32°

2x = 58°

x = 58/2

x = 29°

The larger angle = x + 32 = 29 + 32 = 61°

solving for G

goal is to isolate the variable by undoing in the reverse of the order of operation.

4=2(3g+2)

Answers

Answer:

g = 0

Step-by-step explanation:

4 = 2(3g + 2) ← divide both sides by 2

2 = 3g + 2 ( subtract 2 from both sides )

0 = 3g , then

g = 0

Justin is buying tickets to a concert online from Ticketmaster. He buys 3 tickets that all have the same price.
There is also a service charge, since he is buying it from Ticketmaster, for $5 per ticket. The total cost of his
order was $138.

Answers

Answer:

I don't know if your asking for the price for each ticket, but if you are, it's $41 each.

Step-by-step explanation:

5 x 3 = 15(price of the service charge)

138 - 15 = 123(price with out service tax)

123/3 = 41

Hope this was helpful

Help me solve this please

Answers

Answer:

2/5-1/10 = 3/10

1/5+7/10 = 9/10

Step-by-step explanation:

4/10-1/10 = 3/10

2/10+7/10 = 9/10

Solve.

Write an expression for the total cost (in dollars) of Sam's purchase if he buys x candies costing 39 cents each and y bars of chocolate cost $1.25 each.


a. (0.39 + x) ∙ (1.25 + y)

b. 0.39x + 1.25y

c. 1.64(x + y)

d. 39x + 1.25y

Answers

Answer:

the answer to the question is c

41% of what number is 77

Answers

Answer: 31.57

Step-by-step explanation:

41% of 77 is what?

41% of 77 is Y

Equation: P% * X = Y

Solving our equation for Y

Y = P% * X

Y = 41% * 77

Converting percent to decimal:

p = 41%/100 = 0.41

Y = 0.41 * 77

Y = 31.57

Other Questions
in a water molecule the hydrogen and oxygen atoms hold together by sharing Which is the equivalent of 0.00000000989 in proper scientific notation? The State of Florida has seen an increase in traffic accidents over the past 10 years and has decided to improve traffic safety. Which step in the policy cycle are lawmakers currently on? Policy AdoptionAgenda SettingPolicy FormulationPolicy ImplementationPolicy Evaluation If the legs of an isosceles right triangle have a length of 15 StartRoot 2 EndRoot ft, what is the length of the hypotenuse? 7. 5 feet feet feet 30 feet. 6(2x + 4) = 3(4x + 8)Please answer this! WILL give 100 points if you answer this correctly!!!Refer to the Department of Energy's "Guide to Renewable Energy."How does the word bi-directional affect the meaning of this sentence?In net metering, a single, bi-directional meter records both the electricity the home draws from the grid and the excess electricity the homeowners system feeds back into the grid.A. It explains how a meter measures the electrical power flowing back and forth when a customer has a renewable energy source.B. It tells how customers must still pay even when they have a renewable energy source.C. It introduces the idea that renewable energy can move in more than one direction.D. It describes how renewable energy customers use two meters to measure the energy their system produces and the energy they buy from their power provider. How do you say, "He wants a slice of ham?"O Il veut une tranche de jambon.O Il veut une tranche du jambon.O il veut un peu de jambonO il veut une pice du jambon. Which is a better deal: A can of 3 tennis balls for $3 or a box of 10 balls for $9? In the photoelectric effect a photon with an energy of 5. 3. 3 useful applications of alkaline earth metals a company has an unbiased forecast for its demand. what does that mean? The graph shows the amount of rain that falls over time. Does the rain fall at a constant or variable rate? How much rain falls per hour?thanks! Is there a formula for[tex] {a}^{m} + {a}^{n} [/tex]? Respiratory system anatomy labeling:What is number 8? What does self-government mean? People depend on the laws of another country to govern themselves. Instead of an outside government, people determine laws and government for themselves. People follow the rules of a government that is far away from them. People rely on a smaller government to rule the country and make laws. Think of any text/song/poem/book which you think has a Connection or relationship with each other ______ involves reselling furniture, consigning clothing to resale shops, using cloth shopping bags instead of plastic bags, and bringing your own coffee cup to your local coffee shop. 1)Find the value of x. Choose one of the Psalms listed as a lament. Write your choice below. Using the six-part structure of the lament as described in this Section, examine your Psalm verse by verse and write in the verse numbers that fit with the structure of the lament in the Table provided. NOTE: Some of the Lament Psalms will not have all the parts of this structure, and some parts of the structure may be utilized more than once.Psalm:I. Address to God:II. Lament or Complaint:III. Confession of Confidence:IV. Petition:V. Words of Assurance:VI. Vow or Exclamation of Praise Write the number for twenty-six million seven hundred thousand.