Find the sum of the series: (-2) + (-5) + (-8) + ... + (-20)

Answers

Answer 1

Thus, the sum of the series is 77. Answer: The sum of the series is 77. This answer contains a long answer that has 250 words.

To find the sum of the series (-2) + (-5) + (-8) + ... + (-20), we need to determine the number of terms in the series, and then use the formula for the sum of an arithmetic series,

which is S_n = (n/2)(a_1 + a_n), where S_n is the sum of the first n terms of the series, a_1 is the first term, a_n is the nth term, and n is the number of terms in the series. Here, a_1 = -2, and the common difference, d = -5 - (-2) = -3, so a_n = a_1 + (n-1)d = -2 + (n-1)(-3) = -2 - 3n + 3 = 1 - 3n.

We need to find n such that a_n = -20, which gives 1 - 3n = -20, or 3n = 21, or n = 7.

Therefore, there are 7 terms in the series. Using the formula, S_7 = (7/2)(-2 + (-20)) = (-7)(-22/2) = 77.

Thus, the sum of the series is 77. Answer: The sum of the series is 77.

This answer contains a long answer that has 250 words.

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Related Questions

The right triangle below has legs of length and.
The hypotenuse has length.
Four copies of this triangle are arranged as follows.
The hypotenuses form a square of side length and area.
Answer the questions below to find how, and are related.
Part 1: Compute the total combined area of the four triangles:

Part 2: Compute the area of the large (outer) square:
Part 3: Using your answers in Parts 1 and 2, find the area of the small (inner) square.
Part 4: We are given the side lengths and. Compute.
Part 5: Use, or complete the statement below.

Answers

Answer + explanation:

Part 1: First, find the area of one triangle using the formula base * height / 2. You have base = 10 and height = 7, so area = 7 * 10 /2 = 70/2 = 35. Since you're finding the combined area of 4, you have to do 35 * 4 = 140.

Part 2: To do this, find the side length of the square. Looking at the picture, you see that all you have to do is 10 + 7 = 17 to find one side. Then, to find the area do 17 * 17 = 289.

Part 3: To find the area of the small square, all you do is area of the large square - combined area of 4 small triangles, so 289 - 140 = 149.

Part 4: a^2 = 7 * 7 = 49. Then, b^2 = 10 * 10 = 100. Adding them together, you get 100 + 49 = 149.

Part 5: Since you already have the a^2 + b^2 part, all you need to do is find what c^2 is. You can see in the picture that c^2 equals the area of the small square, which you found in part 3. c^2 = 149. Then, you have 149 and 149, which are equal so the answer is =.

Daniel wants to know the volume of his cube. He notices that the cube 1/5 centimeters side lengths. What is the volume of the cube?

Answers

Answer:

1/125 cm^3

Step-by-step explanation:

Given data

Length of one side = 1/5cm

Required

The volume of the cube

We know that

V= l^3

substitute

V= (1/5)^3

V= 1/125cm^3

Hence the volume is 1/125 cm^3

In ΔRST, the measure of ∠T=90°, TS = 65, SR = 97, and RT = 72. What ratio represents the cotangent of ∠S?

Answers

Answer:

65/72

Step-by-step explanation:

Given that ∠T=90° then the triangle ΔRST is  a right angled triangle. Considering ∠S, RT is the opposite side, TS is the adjacent side and RS is the hypotenuse side. Using the notation

SOH CAH TOA

Tan ∠S = 72/65

Hence the cotangent of ∠S which is the inverse of the tangent will be

= 65/72

Kiran's family took a road trip to Niagara Falls. Kiran slept through the last 62% of the trip. If the total length of the trip was 1000 miles, how many miles had they traveled when Kiran fell asleep?

Answers

Answer:

380 miles

Step-by-step explanation:

First, find 62% of 1,000:

1,000 • .62 = 620 miles

Next, subtract 620 from 1,000:

1,000 - 620 = 380 miles

The family had traveled 380 miles before Kiran fell asleep

the base of a rectangular prism has an area of 1 over 8 ft2 and the height of the prism is 2 over 3 ft. what is the volume of the prism?​

Answers

Answer:  the volume is 1/12 ft³

Step-by-step explanation:

Multiply the area of the base times the height:

1/8 × 2/3 = 2/24 or 1/12

the ft² times ft becomes ft³

So the volume is 1/12 ft³

Tonya and Mario are asked to use a pan balance to find the mass of the same rock. Tonya finds the rock's mass to be 680 grams. Mario finds the rock's mass to be 672 grams. Which is the best explanation for the difference in their measurements?


A. Either Mario or Tonya measured the mass of the rock incorrectly on the pan balance.


B. The rock was cold when Tonya measured its mass and hot when Mario measured in mass.


C. The rock changed in size between the time Tonya measured it and the time Mario measured it.


D. The rock broke before Mario measured it. So the mass of the two pieces together was less than when Tonya measured it. PLEASEEEE HELPPP

Answers

B is the answer B is the answe

Can some one solve this

Answers

Answer:

J Monica is right

Step-by-step explanation:

Add three to both sides, divide by 4 you get x[tex]\geq[/tex]4

Answer:

J

Step-by-step explanation:

Your garden has 9 pots that use 2 1/3 bag of soil. How much soil does each pot hold? ​

Answers

Answer:

2 6/7

Step-by-step explanation:

i divided

What’s the volume of this cube?

Answers

Answer:

Formula: V = a^3

a = 2in

Input: V = a^3 = 2^3 = 8

Step-by-step explanation:

3/11 as a decimal equivalent

Answers

0.27 repeated with the line over the 27

Answer:

The decimal form for this is 0.27 (With a line on top of it.)

Step-by-step explanation:

See this image:

Find the length of AD if AB = 24, DE = 8, and DC = 12.
a.8
b.12
c.14
d.10

HELP PLS

Answers

Answer:

AD = 12

Step-by-step explanation:

Find the diagram attached

From the given diagram, it can be inferred that;

AB = AD+DB and AD = DB

AB = AD + AD

AB = 2AD

AD = AB/2

Given that AB = 24

AD = 24/2

AD = 12

Hence the length of AD is 12

Answer: 10

Step-by-step explanation:

I got it right after trying the answer of 12 on CAOLA

Help Please........ ​

Answers

Answer:

4

Step-by-step explanation:

Answer:

12

Step-by-step explanation:

(4 x 2)/2 + (4 x (6-2))/2 = 12

Convert the decimal below to a fraction in simplest form. 0.689

Answers

Answer:

689 / 1000 is the answer

Step-by-step explanation:

zzzzzzzzzzzzz

which one pls help me i’ll give extra points

Answers

Answer:

C

Step-by-step explanation:

Answer:

A. The doctors will give Charlie an operation

Step-by-step explanation:

what does the ! after a number mean.
explain in your own words and give 5 examples.

Answers

Answer: it means that you multiply the number by the numbers counting to 0

Step-by-step explanation:4!=4•3•2•1

I NEED HELP WITH THESE ASAP!

Answers

Answer:

I can not see it

Step-by-step explanation:

All movies until 4:00 PM require a discount tiket, and all the movies after 4:00 Pm require a regular -price ticket. Each theater at the movieplex seats 98 people. What is the least number of showings the theater could have shown after 4:00 PM last saturday?

Answers

Answer:

4 shows

Step-by-step explanation:

The theater has 7 cinemas and all of them has capacity of 98 seating. The theater offers discount before 4.00 and there it runs 3 shows before 4 pm in each cinema, after 4.00 pm the theater has capacity of running 4 more shows in each cinema without discount on the tickets.

Solve this equation
12y = 30

Answers

Answer:

hI!!

Y = 5/2

Step-by-step explanation:

Let's solve your equation step-by-step.

12y=30

Step 1: Divide both sides by 12.

12y/12 30/12

the answer for this problem is y=5/2

A baseball player earns $3 million in 2015. During the next 15 years, the earnings increase 4% each year.

a. Write an exponential growth model giving the earnings y (in millions of dollars) t years after 2015. Write the base of the model as a decimal.

An exponential growth model is y=
b. In which year will the player's earnings first exceed $5,000,000?

Answers

Answer:

[tex]y=3*1.04^{t}[/tex]

in 2029

Step-by-step explanation:

[tex]y=3*1.04^{t}[/tex]

[tex]when y=5\\t=\frac{ln(5/3)}{ln(1.04)} =13.02 ..[/tex]

have to round it up to 14 to exceed

Which polynomial represents the difference below?
2x +7X+6
(3x? – X
A. - x + 6x + 6
B. 2x2 + 4x + 6
c. 2x2 + 5x + 6
D. - x2 + 3x + 6

Answers

Answer:

-x²-8x+6

Step-by-step explanation:

Given the polynomial expression

2x²+7x+ 6 and 3x² – X

Taking their difference

2x²+7x+ 6  - (3x² – X)

2x²-3x²+7x+x+6

-x²-8x+6

Hence the required difference is -x²-8x+6

Answer:

-x²+8x+6

Step-by-step explanation:

Ape-x

Which equations are correct?

Select each correct answer.




−4b3(5b2+3)=−20b6−12b3

−6y4(4y2+2)=−24y8−12y4

−5a4(2a2+4)=−10a6−20a4

−4x2(2x2+5)=−8x4−20x2

Answers

Option C

-5a⁴(2a² + 4)

-10a⁶ - 20 a⁴

aye anyone please help me with my math its really easy 9th grade I just figure out part of this question !!! please help

Answers

Answer:

hope this helps!

Step-by-step explanation:

which equation has a solution x= -3
A) 2x - 7 = -1
B) 3x + 8 = 1
C) 1/2x + 8 = 10
D) 1/2(2x - 6) = -6

Answers

Answer:

D

Step-by-step explanation:

1/2 ( 2x - 6) = -6

1/2 = 0.5

0.5(2x-6) = -6

1x-3=-6

1x=-6+3

x=-3/1

x=-3

Answer is D

Step by step:

1/2(2x - 6) = -6
-6 -6
1/2 (-12) = -6
-6 = -6

can someone explain how to solve this please my midterms tomorrow! :)

Answers

Answer:

Step-by-step explanation:

You park in a garage 3 floors below ground level. Then you get in the elevator and go up 12 floors. What floor do you get off the elevator?

Answers

Answer: (B) 6 floors

Step-by-step explanation: Use the equation -3 + 9 to get the amount of floors above ground level.

-3 + 9 = 6

6 floors.

If this helps may I please have a brainliest.

Answer:

you would get off at the 9th floor because in order to reach ground level again your would already go up 3 of the 12 floors. leaving 9 floors left to go up.

Step-by-step explanation:

-3+12=9

help me please I need help

Answers

Answer:

D) 6 in x 4 in

Step-by-step explanation:

3" x 2" scaled up to 1:20 would be 60" x 40"

60" x 40" scaled back to 1:10 would be 6" x 4"

also the scale factor 1:20 is double the scale factor of 1:10

Transform to slope-intercept form. 1+2y=6x-3

Answers

Hello the slope intercept form is y=3x-2

Answer: Y=3X-2

Step-by-step explanation:

First you are gonna need to combine all like factors.

1+2y=6x-3 (subtract 1 from both sides)

2y=6x-4

Then you need to get the y by itself.

2y=6x-4 (divide all terms by 2)

y=3x-2

now you are in slope intercept form (y=mx+b)

Figs come in 2.4 lb bags. Apples come in 7.2 lb bags. How many times as many pounds are the apple bags as the fig bags?

Answers

Answer:

3 times as many pounds

Step-by-step explanation:

7.2 / 2.4 = 3 times as many pounds

Hope that helps!

A company has 200 employees there are 150 female employees. 40 employees are under the age of 20. The probability of randomly selecting an employee who is female or is under the age of 30 is 85%. What is the probability of randomly selecting an employee who is female and under the age of 30?

Answers

Answer and explanation:

Probability= number of favorable outcomes/ total number of outcomes

Probability of selecting an employee who is female= number of female employees/ total number of employees

Probability of selecting an employee who is female= 150/200

Probability of selecting an employee who is under 30= number of employees under 20/ total number of employees

Probability of selecting an employee who is under 30 = 40/200

Probability of randomly selecting an employee who is female and under the age of 30= Probability of selecting an employee who is female × Probability of selecting an employee who is under 30

Probability of randomly selecting an employee who is female and under the age of 30= 150/200×40/200=15/20×4/20=3/20= 0.15

Therefore there's a 15% chance of selecting an employee who is female and under the age of 30

Please help due today

Answers

Answer:

It's gotta be either A or B because C and D don't even make up a square.

I believe that it's one of those ( A or B).

Step-by-step explanation:

Sorry I couldn't help you all the way through to the answer. Hope this helps though! :)

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