Find the sum of the arithmetic sequence 1, 3, 5, 7, … , 99.

Answers

Answer 1

The sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525

What is Sequence?

Sequence is an enumerated collection of objects in which repetitions are allowed and order matters.

Given sequence is 1, 3, 5, 7, … , 99.

It is a arithmetic sequence, the difference between two consecutive terms will be same

d=3-1=2

first term a=1

l=last term =99

We need to find 99 is which term in the sequence

Aₙ = a + ( n - 1 ) d

99=1+(n-1)2

99=1+2n-2

99=2n-1

100=2n

Divide both sides by 2

50=n

Now we need to find the sum of 50 terms

Sₙ=n/2(l+d)

=50/2(99+2)

=25(101)

=2525

Hence, the sum of the arithmetic sequence 1, 3, 5, 7, … , 99 is 2525

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Related Questions

Which expression is equivalent to 27 + 63 ? 3(9 + 18) 9(3 + 7) 21(7 + 3) 7(21 + 9)

Answers

Which expression is equivalent to 27 + 63 ?

3(9 + 18)

9(3 + 7)

21(7 + 3)

7(21 + 9)

nswer the question.
The table shows the amount of fabric needed to make each item of doll clothes. Tamara is making 5 of
Fabric for Doll Clothes
Item Amount of Fabric Needed (feet)
Blouse2/12
Jacket 7/12
Skirt 7/12
How many feet of fabric are needed to make 5 of each item? Move numbers to the boxes to show the answer. If there is no whole number
put a 0 in the first box.

Answers

Equation:

5 x (2/12 + 7/12 + 7/12) = f                    f = amount of fabric needed

Solve:

10/12 + 35/12 + 35/12 = f

80/12 = f

Simplify:

6 8/12

Answer:

Tamara needs 6 ft and 8 inches of fabric to make five of each item.

What is the value of Negative 3 squared + (negative 4 + 7) (2)?
–28
–3
3
15
I am on a unit test hurry please

Answers

-3^2+(-4+7)(2)

answer = 15

Answer:

15

Step-by-step explanation:

a negative number squared is positive, so its 9 + (-4 + 7)*2. 7-4 is 3, which we then multiply by 2 to get 6. Now add that to 9 to get 15.

Hope this helps!

On Saturday, the Milleman Family had dinner at a restaurant. They ordered 3 pizzas and 2 cheeseburgers for $41.50. The following weekend, the Anderson Family had dinner at the same restaurant where they ordered 2 pizzas and 5 cheeseburgers for $43.25. Which system of equations can be used to determine the cost of one pizza (p) and one cheeseburger (c)?

Answers

Answer:  $8.64 and $7.79 respectively.

 

Step-by-step explanation: To determine the cost of one pizza and one cheeseburger, we can set up the following system of equations:

3p + 2c = 41.50

2p + 5c = 43.25

The first equation represents the total cost of the Milleman Family's meal, where 3p represents the cost of 3 pizzas, 2c represents the cost of 2 cheeseburgers, and 41.50 represents the total cost of the meal. The second equation represents the total cost of the Anderson Family's meal, where 2p represents the cost of 2 pizzas, 5c represents the cost of 5 cheeseburgers, and 43.25 represents the total cost of the meal.

By solving this system of equations, we can determine the cost of one pizza and one cheeseburger. For example, we can use the elimination method to solve the system of equations as follows:

First, we can multiply the first equation by 5 and the second equation by 3 to get the following equations:

15p + 10c = 207.50

6p + 15c = 129.75

Next, we can subtract the second equation from the first equation to eliminate the c terms and find the value of p as follows:

15p + 10c = 207.50

6p + 15c = 129.75

9p = 207.50 - 129.75

9p = 77.75

p = 77.75 / 9

p = 8.64

Finally, we can substitute the value of p that we found into one of the original equations to find the value of c as follows:

3p + 2c = 41.50

3(8.64) + 2c = 41.50

25.92 + 2c = 41.50

2c = 41.50 - 25.92

2c = 15.58

c = 15.58 / 2

c = 7.79

Therefore, the cost of one pizza is $8.64 and the cost of one cheeseburger is $7.79.

Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral.​

Answers

Refer to the photo taken.

18=6h+2h pls help me with this answer im not understandin it

Answers

Answer:2.25 or 9/4

first we need to add 6h and 2h together, and we get 8h, and we divide 8 both side will get the fraction 18/8 and we can simplify will get 9/4 if you want more simple and will become 2.25

Algebra
will mark brainliest

Answers

The inequality for which the order pair (-5, -7) is a solution will be x + y ≤ 3. Then the correct option is B.

What is inequality?

Inequality is defined as an equation that does not contain an equal sign. Inequality is a term that describes a statement's relative size and can be used to compare these two claims.

Let's check all the options, then

A)  y ≤ (1/4)x - 1

At (-5, -7), we have

-7 ≤ (1/4)(-5) - 1

-7 ≤ -2.25

This is incorrect.

B)  x + y ≤ 3

At (-5, -7), we have

-5 + (-7) ≤ 3

-12 ≤ 3

This is correct.

The inequality for which the order pair (-5, -7) is a solution will be x + y ≤ 3. Then the correct option is B.

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A professor had students keep track of their social interactions
for a week. The number of social interactions over the week is
shown in the grouped frequency distribution. Identify the lower
limit of the fifth class.
The lower limit of the fifth class is
(Type a whole number.)

Answers

The lower limit of the fifth class for the track of social interactions

for a week is 50.

Explain the term lower limit of the class?The frequency distribution has an upper class limit and a lower class limit for each class.The smallest data point that really can correspond to a class is known as the lower class limit. The largest data object that can be a member of a class, or upper class limit.

Allow the class intervals to be 30 - 34, 35 - 39, 40 - 44, 45 - 49, 50 - 54, etc. for some aggregated data.

In this case, the distribution is continuous, and all of the class intervals overlap.

Fifth class ; 50 - 54,

The class boundaries of the range from 50 - 54, 50 is the lower limit while 54 is the upper limit.

Thus, the  lower limit of the fifth class for the track of social interactions

for a week is 50.

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At as sale, suits were sold for $72 each. This price was 45% of a suits original price. How much did a suit originally cost?

Answers

Answer: 1680. The answer is 1680 because 56% of 3000 is 1680 people.

Answer:

The suit orginally costed $160 dollars.

Step-by-step explanation:

Find the quadratic equation whose parabola has vertex (3, –2) and y-intercept (0, 16). Give your answer in vertex form, and show your work.
Please Help!!

Answers

Answer:

y = 2(x-3)^2-2

Step-by-step explanation:

We can find the quadratic equation by using the vertex form.  The vertex form of a quadratic equation is:

[tex]y=a(x-h)^2+k[/tex], where x and y are any point on the parabola, a is the constant (indicating whether the parabola opens up or down), and h and k are the coordinates of the vertex.

Since we already have the y-int (an x and y coordinate lying on the parabola) and the vertex, we can plug in both to find a:

[tex]16=a(0-3)^2-2\\16=a(-3)^2-2\\16=9a-2\\18=9a\\2=a[/tex]

Thus, the equation is:

[tex]y=2(x-3)^2-2[/tex]

Will give brainliest

Answers

Answer:

-5

Step-by-step explanation:

y (4) need to times 2.5 to be 10

so, x (-2) needs to times 2.5 to be the answer

-2 * 2.5 = -5

Can someone help me with this?

Answers

-6 because -10 is 6. -5 is 3. 0 is 0. 5 is -3. 10 is -6

The ratio of brownies to cookies is 3:5. If there are 75 cookies, how many brownies are there?
Group of answer choices

45

15

60

32

Answers

Answer:

15:25 or 15 brownies

Step-by-step explanation:

25 / 5 = 5 (scale factor)

3 * 5 = 15

What occurs when you are dealing with objects that are round
static friction
sliding friction
rolling friction​

Answers

rolling friction because an object that is round is rolling

Add a term to the expression so that it becomes a perfect square trinomial.
x2-22x +

Answers

Answer:

Step-by-step explanation:

is times 43

You decide to buy a refurbished computer for $550.00 plus 6% sales tax. BB Electronics allow you to take out a no-interest loan for 12 months, and after that the interest rate is a 13.25% APR. You must make payments of $25/month, and if you miss one payment you are assessed a late fee of $29.00 plus 13.25% APR interest beginning from the date of purchase.

You missed the second payment. What is the amount of interest of the bill you will receive?

Answers

The interest on the bill will be calculated as follows:

Amount of Loan = $550

Sales Tax = 6% of $550 = $33

Total Loan = $550 + $33 = $583

Interest = 13.25% APR x $583 = $77.13

Late fee = $29

Total Interest = $77.13 + $29 = $106.13

find the slope and y-intercept of the line 3x - 5y = 15

Answers

The slope of the given line, 3x - 5y = 15, is 3/5 and the y-intercept is -3

Determining the slope and y-intercept of a line

From the question, we are to determine the slope and y-intercept of the given line.

The given line is

3x - 5y = 15

To determine the slope, we will write the equation in the slope-intercept form of a line.

The slope-intercept form of a line is given as

y = mx + b

Where m is the slope

and b is the y-intercept

Now, we will express the given equation in this form

3x - 5y = 15

-5y = 15 - 3x

Divide through by - 5

y = -3 + 3/5x

y = 3/5x - 3

By comparing to the slope-intercept form of a line,

m = 3/5

and b = -3

Hence, the slope is 3/5 and the y-intercept is -3

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John brings $15 to the candy store. He buys a bag of jelly beans for $4 and plans to buy some chocolate that costs $5 per pound. Write an inequality to solve for all the possible values of x, the number of pounds of chocolate John could buy.

Use the on-screen keyboard to type the inequality that represents this situation in the box below.

Answers

Answer:

Step-by-step explanation:

he could buy 2 pounds of chocolates and save $1.

Mia is traveling from her house to her sister’s home. She took the bus to the car rental lot and is now driving the rest of the way at a constant rate of speed. What does the -intercept represent in this problem?
the distance (mi) that Mia traveled on the bus to the car rental before she started driving the car
the distance (mi) that Mia traveled from the car rental lot to her sister's home
the amount of time (hr) elapsed for every mile the car travels from the car rental lot
the distance (mi) the car travels from the car rental lot for every 1 hour elapsed

Answers

Answer:

The distance (mi) the car travels from the car rental lot for every 1 hour elapsed.

Step-by-step explanation:

A cafeteria sold 36 cartons of regular flavored milk. If the ratio of regular milk sold to chocolate milk sold was 9:4, what is the combined amount of chocolate and regular milk sold?

Answers

Answer:

The combined amount of chocolate and regular milk sold was 52 cartons.

Step-by-step explanation:

1. Divide

36 ÷ 9 = 4

(This means that the ratio has a unit rate of 4. That means):

2. Second ratio rate

4 x 4 = 16

(Because the unit rate is 4).

3. Add

(Now, we add the original 36 cartons with the 16 cartons we found because the first step was just for finding the unit rate).

36 + 16 = 52 cartons.

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Given the ratio 8 ounces to 1 cup,how many ounces are in 4 cups?

Answers

Answer:

32 oz

Step-by-step explanation:

Given the ratio 8 ounces to 1 cup, how many ounces are in 4 cups?

4 * 8 oz = 32 oz

describe the sampling of p hat. Assume that the size of the population is 25000 n= 300 p=0.7

Answers

The mean of the given sample data is 210, and the standard deviation is 7.937.

Given size 'n' = 300

The population proportion 'p' = 0.7

Let 'x' be the random variable of the binomial distribution

a)  mean of the binomial distribution  = n p = 300 × 0.7

                                                              μ  = 210

b)  variance of the binomial distribution

⇒ n p q

⇒ 300 × 0.7 ×0.3

⇒ σ² = 63

The standard deviation of the binomial distribution:

⇒ √n p q = √63 = 7.937

Thus, the mean of the given sample data is 210, and the standard deviation is 7.937.

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The question seems to be incomplete the correct question would be:

describe the sampling of p hat. Assume that the size of the population is 25000 n= 300 p=0.7 a) Determine the mean of the sampling distributionb) Dtermine the standard deviation of the sampling distribution

The perimeter of a rectangle is 54 inches and the length of one of its sides 6 inches. What is the combined length of the other three sides, in feet?

Answers

Answer:

4 ft

Step-by-step explanation

the combined length of the other three sides can be found with 54-6 is 48 inches

48 inches can be turned into feet by dividing by 12.

48in / 12=4ft

You withdraw $375 from your bank account. You receive a stack of 24 bills consisting of $5, $10, and $20 bills. The number of $5 bills is one-half the number of $10 bills. How many of each type of bill do you receive?

Answers

The number of $ 5 bills = 3

The number of $ 10 bills = 6

The number of $ 20 bills = 15

What is an Equation?

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the total amount be = $ 375

Let the total number of bills = 24

Let the number of $ 5 bills be = x

Let the number of $ 10 bills be = y

Let the number of $ 20 bills be = z

The total number of $ 5 bills x = ( 1/2 ) x number of $ 10 bills

So , x = y/2

Now , the equation will be

The total number of bills = x + y + z

So , x + y + z = 24   be equation (1)

And ,

The total amount = 5x + 10y + 20z

So , 5x + 10y + 20z = 375

Divide by 5 on both sides , we get

x + 2y + 4z = 75   be equation (2)

On simplifying equation (1) and equation (2) , we get

x + y + z = 24

Substituting the value of y , we get

x + 2x + z = 24

3x + z = 24   be equation (3)

And ,

x + 2y + 4z = 75

x + 4x + 4z = 75

5x + 4z = 75   be equation (4)

Multiply equation (3) with 4 , we get

12x + 4z = 96   be equation (5)

Subtract equation (4) from equation (5) , we get

7x = 21

Divide by 7 on both sides , we get

x = 3

Therefore , the number of $ 5 bills is 3

Substitute the value of x , we get

y = 2x

y = 6

Therefore , the number of $ 10 bills is 6

Substitute the value for x and y in equation (1) , we get

x + y + z = 24

3 + 6 + z = 24

z + 9 = 24

Subtract 9 on both sides , we get

z = 15

Therefore , the number of $ 20 bills is 15

Hence ,

The number of $ 5 bills = 3

The number of $ 10 bills = 6

The number of $ 20 bills = 15

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5. -4h + 3 + Th ≥ 9h - 21

Answers

Hope this helps you and was the number 5 part of the problem ? If yes lmk I’ll correct the answer

(3.76x 10-8 )-(2.94 x 10-8)
Write your answer in scientific notation

Answers

Hope this helps you

Suppose you go to work for a company that pays one penny on the first day, 2 cents on the second day, 4 cents on the third day and so on.
Hint: use an= a1 (r)^n-1 and Sn= a1 (1-r^n) / 1 - r

A. If the daily wage keeps doubling, what would your income be on day 31? Give your answer in dollars NOT pennies.
Income on day 31 = $ __________

B. If the daily wage keeps doubling, what will your total income be for working 31 days? Give your answer in dollars NOT pennies.
Total Income for working 31 days = $ _________

Answers

a. Your income on the 31st day is given as follows: $10,737,418.24

b. Your total income for working 31 days is of: $21,474,836.47

What is a geometric sequence?

The definition of a geometric sequence is given as follows:

[tex]a_n = a_1(r)^{n - 1}[/tex]

In which the terms are given as follows:

[tex]a_1[/tex] is the first term.r is the common ratio of the sequence.

In a geometric sequence, each term is the multiplication of the previous term by the common ratio.

The sequence in this problem is given as follows:

(0.01, 0.02, 0.04, ...).

Hence the first term and the common ratio of the sequence are given as follows:

[tex]a_1 = 0.01, q = 2[/tex]

Thus the definition is of:

[tex]a_n = 0.01(2)^{n - 1}[/tex]

The income on the 31st day is of:

[tex]a_{31} = 0.01(2)^{30} = 10,737,418.24[/tex]

The sum of the first n terms of a geometric sequence is given as follows:

[tex]S_n = a_1\frac{1 - r^n}{1 - r}[/tex]

Then the sum of the first 31 terms is of:

[tex]S_{31} = 0.01\frac{1 - (2)^{31}}{1 - 2} = 21,474,836.47[/tex]

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Isaiah is trying to buy dry-erase markers for his teachers during teacher appreciation week. He
is able to collect 12 markers a day and started off with 15. How many days will it take him to get
to 135 markers? Make an equation to solve the problem using m for markers and d for days.

Answers

Answer:

It will take him 10 days to get to 135 markers.

[tex]d=12m+15[/tex]

Step-by-step explanation:

(attached)

Solve for m.

m+15<−123
Responses

m>−11315
m is greater than negative 1 and 13 over 15

m>−1715
m is greater than negative 1 and 7 over 15

m<−1715
m is less than negative 1 and 7 over 15

m<−11315
and show work

Answers

The solution to the inequality is m < −1 13/15 . m is less than negative 1 and 7 over 15

How  to solve for the inequality

In this question we have to solve for the inequality that is given as m + 1/5 < -1 2/3

We would have to rewrite the equation using the math tool

[tex]m +\frac{1}{5}\leq 1\frac{2}{3}[/tex]

The mixed fraction can be properly rewritten  as improper fraction

[tex]m +\frac{1}{5}\leq \frac{5}{3}[/tex]

subtract 1/5 from 5/3

[tex]m\leq -\frac{5}{3} -\frac{1}{5}[/tex]

we have to carry out the subtraction of the fraction

[tex]m < \frac{-25-3}{15}[/tex]

[tex]m < \frac{-28}{15}[/tex]

This can be written in mixed fraction as

[tex]m < -1\frac{13}{15}[/tex]

Hence the solution of m is D. m < −1 13/15

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Complete question

m + 1/5 < -1 2/3

Responses

A. m > −1 13/15

m is greater than negative 1 and 13 over 15

B. m > −1 7/15

m is greater than negative 1 and 7 over 15

C. m < −1 7/15

m is less than negative 1 and 7 over 15

D. m < −1 13/15

m is less than negative 1 and 7 over 15

chris is 5 years older than 4 times arins age. the sum of their ages is less than 40. what is the oldest arin could be?

Answers

Answer: 6 years old.

Step-by-step explanation:

Chris: 5+4a

c + a<40

5 + 4a + a < 40

5a<35

a<7

For the oldest, let's assume Arin is 6, because it is the highest number that is less than 7.

Arin can be maximum of 6 years old.

What is Algebra?

A branch of mathematics known as algebra deals with symbols and the mathematical operations performed on them.

Variables are the name given to these symbols because they lack set values.

In order to determine the values, these symbols are also subjected to various addition, subtraction, multiplication, and division arithmetic operations.

Given:

Let the Arin's age be x.

So, Chris age is 4x + 5

Now, the sum of their ages is less than 40.

x+ 4x+ 5 < 40

5x < 35

x < 7

Hence, Arin can be maximum of 6 years old.

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