The given series has six terms. What is the sum of the terms of the series? 1 + 3 + 5 + . . . + 11

Answers

Answer 1

The rule is +2, so first we find the other two terms.

5 + _ + _ + 11

To find them, add 2 to 5, which gives us 7, so the 4th term is 7, and then add 7 +2, which gives 9, so 9 is the 5th.

Now add all: 1 + 3 + 5 + 7 + 9 + 11 = 36

Your answer is 36.

Answer 2

Answer: The required sum of the terms is 36.

Step-by-step explanation: We are given that the following series has six terms :

1 + 3 + 5 + . . . + 11.

We are to find the sum of the terms of the series.

We see the following pattern in the consecutive terms of the series :

[tex]3-1=5-3= ~~.~~.~~.~~=2.[/tex]

So, the given series is an ARITHMETIC series with fist term 1 and common difference 2.

We know that

the sum of first n terms of an arithmetic series with first term a and common difference d is given by

[tex]S_n=\dfrac{n}{2}(2a+(n-1)d).[/tex]

For the given series,

first term, a = 1 and common difference, d = 2.

Therefore, the sum of first six terms will be

[tex]S_6=\dfrac{6}{2}(2\times 1+(6-1)\times2)=3(2+5\times2)=3(2+10)=3\times12=36.[/tex]

Thus, the required sum of the terms is 36.

Related Questions

The area of a rectangle rug is (3x + 9) square units.Factor (3x + 39) to find possible dimension of the rug.?

Answers

Would be the (3x+39) factored out

3(x+13)

The possible dimension of the rug will be 3 and (x + 3).

What is expansion?

Expanded form is the term used in mathematics to refer to the process of expanding a number to convey the value of every digit and place value.

In mathematics, every real-world issue may be transformed into an equation, sometimes in the form of a factor, which must then be expanded to get a solution.

If you solve a factor by opening the bracket then you will go to get on some expanded term called expansion.

Area of rectangle = length × width

Given,

Area of rectangle rug = (3x + 9)

So,

length × width = (3x + 9)

length × width = 3(x + 3)

So out of 3 and (x + 3), one would be the length and one would be the width.

For more information about the expansion

brainly.com/question/14447197

#SPJ5

Steve earned 60 dollars and spent 2/3 of it. How much did he spend?

Answers

This is very easy! all you have to do is divide 60 by 3 then multiply that number by 2 to get your answer.

60* 2/3 = 60/1 x 2/3 =120/3

120/3 = 40

he spent $40

Find two positive fractions with a quotient of 5/6

Answers

Alright, so if we divide fractions we get
(x/y)/(a/b)= (x/y)*(b/a). If the x is 5 and the a is 6, as well as y and b being the same therefore cancelling out, we can write it easily. For example, we can write (5/100)/(6/100) or (5/60)/(6/60)

A pyramid and prism have the same base area and height. The prism's base area is 8 square units and its height is 16 units. What is the volume of the pyramid? The volume of the pyramid is __________ cubic units. Enter the number that correctly fills in the blank in the previous sentence.

Answers

Prism dimensions:
8 units² (base area)
16 units (height)

Because the dimensions are the same...

Pyramid dimensions:
8 units² (base area)
16 units (height)

The volume for a pyramid = 1/3 ba * h

Substitute and solve.

1/3 8 * 16
= 1/3 (128)
= 42.66...

Therefore the volume is approximately 42.67cm³

The volume of the pyramid with a base area of 8 square units and a height of 16 units is 42.67 cubic units.

The volume of a pyramid is calculated as one-third of the base area times the height. The base area of the given pyramid is 8 square units and the height is 16 units. Using the formula for volume V = rac{1}{3}Ah, where A is the base area and h is the height, the volume of the pyramid can be found as follows:

V = rac{1}{3} imes 8 imes 16

V = rac{1}{3} imes 128

V = 42.67 cubic units (rounded to two decimal places).

Therefore, the volume of the pyramid is 42.67 cubic units.

What's equivalent to 3(8+7) 24+7 24+21 Please help

Answers

24 +21
The distributive property dictates that a(b+c)= ab+ac
So 3(8+7)= 3(8)+3(7)

David and Amanda are trying to figure out how long they can live off their $12,350 savings if they spend $240 each month. They have each created an equation.

David's Equation Amanda's Equation
y = 12,350 - (240x) y = 12,350 + (240x)

Which person has the correct equation to model this linear relationship? (4 points)

a) Amanda's equation is correct, because their spending will be multiplied by the number of months and then added to their savings.

b) Amanda's equation is incorrect, because their spending will increase the amount of their savings.

c) David's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings.

d) David's equation is incorrect, because their spending should be a fixed amount and should not be multiplied.

Answers

C. David's equation is correct, because their spending will be multiplied by the number of months and then subtracted from their savings.

Bernard counted 8 posts along the side of the road. If the posts were 20meters apart how far is the first post from the last

Answers

There will be seven spaces between the 1st and the 8th post.
The distance between posts is 20 meters
The distance between the 1st and the 8th post is 20×7 = 140 metres

The diagonal of a square unit is x units. What is the Area of the square in terms of x

Answers

The diagonal of a square is:

d^2=s^2+s^2

d^2=2s^2 we are told that d=x so

x^2=2s^2

s^2=(x^2)/2

And since the area of a square is s^2, the area of this square is:

(x^2)/2

Or as it is shown in your answer choices...

(1/2)x^2 square units (the top answer :P)

The area of a square with a diagonal x is (1/2)x² unit²

Square

A square is a quadrilateral (has four sides and four angles) in which opposite sides are equal and parallel. All the sides of a square have the same length and each angle measure 90 degrees.

let l represent the length of the side of the square and x be the length of the diagonal. Using Pythagoras theorem:

l² + l² = x²x² = 2l²l = x√(1/2)

Area of square = l * l = x√(1/2) * x√(1/2) = x² * 1/2 = (1/2)x² unit²

The area of a square with a diagonal x is (1/2)x² unit²

Find out more on square at: https://brainly.com/question/8429946

help again pleaseeeeeeejshfhfuuffufuf

Answers

I think it's the last one:
Grade number and type of instrument

Which of the following coordinates of point C would make triangle ABC similar to triangle LMP ? Look at pic attached :) thank you .

Answers

The triangle ABC is similar to triangle LMP. The order here is very important. The letters correspond to one another
A corresponds to L (first letters of each sequence)
B corresponds to M (second letters of each sequence)
C corresponds to P (third letters of each sequence)

In a similar fashion, the segments also correspond to one another.
AB corresponds to LM (first two letters of each sequence)
AC corresponds to LP (first and last letters of each sequence)
BC corresponds to MP (last two letters of each sequence)

------------------------------------

AB corresponds to LM. AB is 4 units long. LM is 2 units long. So AB is twice as long as LM. This ratio (of 2:1) will be applied to every paired corresponding value.

Also, the right angle is at angle M for triangle LMP. The right angle will be at angle B for triangle ABC (since B corresponds to M). The answer will have an x coordinate of 7. So the answer is either choice B or choice C.

If we move 4 units down from point B, we land on (7,-10). That isn't listed as an answer choice. Let's try moving 4 units up from point B. We land on (7,-2). This is an answer choice

So the final answer is choice C) (7,-2)

a right prism with a base perimeter of 9 units a height of 5 units and a total base of 16 square units has a surface area of how many square units?

Answers

the answer is 80 because of 16 times 5 that's how you get your answer

hope this helps :)

Ralph sold brownies for $0.27 a piece in order to earn money to buy baseball cards. If the cards cost $0.54 per pack, and if Ralph had no money left over after buying them, what is the least number of brownies he must have sold?

Answers

2 pieces because $0.27 times 2 is $0.54.

Which unit rate is the lowest price per ounce? Choice A: 25 ounces of potato chips for $3.49 Choice B: 40 ounces of potato chips for $4.79 Choice A Choice B The unit rates are equal. The unit rates cannot be determine

Answers

choice A : 3.49/25 = 0.139 rounds to 14 cents per oz
choice B ; 4.79/40 = 0.119 rounds to 12 cents per oz

lowest price is choice B

Answer:

B is the lowest price per ounce

Step-by-step explanation:

choice A is 14 cents per ounce, and choice B is 12 cents per ounce.

HELPPP PLEASEEEEEE!?!?!

Answers

a straight line is 180 degrees so we can find C by subtracting 140 from 180

180-140 = 40 degrees

all 3 inside angles need to equal 180 so now we have

180 = 40 + (2x) + (x+2)

180 = 40 +3x +2

180=42+3x

138=3x

x= 138/3 = 46

check : 2x= 2*46 = 92

x+2 = 46+2 = 48

92 +48 +40 = 180

so x = 46 degrees

so angle B = 2x46 = 92 degrees

Which class has 32% girls?

Answers

a is the answer i belive

the answer to this question is beginning soap

BEST ANSWER GETS BRAINLIEST
Which of the following sets shows all the numbers from the set {3, 4, 5, 6} that are part of the solution to the equation 5x + 4 < 29?

Answers

3 and 4 can equal x but 5 and 6 can't

You simply substitute each number in to see if it's true. First, try 3.
5x + 4 < 29 now becomes :
5(3) + 4 < 29.
Simplify.
15 + 4 < 29
Simplify again.
19 < 29
This statement is true, so 3 works.
Now try 4.
5(4) + 4 < 29
Simplify
20 + 4 < 29
Simplify again
24 < 29
This statement is true, so 4 works.
Now try 5.
5(5) + 4 < 29
Simplify
25 + 4 < 29
Simplify again
29 < 29
This is not true, so 5 doesn't work. This means 6 also doesn't work.
*** So your answers are 3 and 4 ***

The sum of 2/9 and 2 5/9 in simplest form is

Answers

2/9 + 2 5/9
Add the fractions first:
2/9 + 5/9 = 7/9
2 7/9

Answer:

2 7/9

Step-by-step explanation:

solve the inequality 6x<18

Answers

Divide both sides by 6 to isolate variable

6x/6<18/6
x<3

Final answer: x< 3

Tony is making small bags of bird sees from a larger bag that weighs 11.16 pounds. If he puts the same amount of seed in each of 6 bags, how much will each bag weigh?

Answers

Tony is dividing the larger bag of bird seeds into 6 smaller bags equally. So, we will divide by 6.

11.16 / 6 = 1.86

So, each smaller bag of bird seeds will weigh 1.86.

An empty rectangular tank, 40 cm long and 25 cm wide, contains 2 metal cubes of edge 10 cm. the tank is being filled with water flowing from a tap at a rate of 10 liters per minute. If it takes 3 minutes to fill up the tank, find the height of the tank.

Answers

Final answer:

The height of the tank is 0.5 cm.

Explanation:

To find the height of the tank, we can use the formula:

Volume of water = base area × height

The base area of the tank can be found by multiplying the length and width: 40 cm × 25 cm = 1000 cm².

The volume of water flowing from the tap is given as 10 liters per minute, which is equivalent to 10000 cm³ per minute or 166.667 cm³ per second. Since it takes 3 minutes to fill up the tank, the total volume of water will be 3 minutes × 166.667 cm³ per second = 500 cm³.

Now, we can plug these values into the formula to find the height:

500 cm³ = 1000 cm² × height

Dividing both sides by 1000 cm² gives:

height = 0.5 cm

Therefore, the height of the tank is 0.5 cm.

To find 19+(11+37) Lennie added 19 and 11. Then he added 37 to the sun.what property did he use

Answers

Normally, when you apply the PEMDAS (Parenthesis, Exponent, Multiplication, Division, Addition, Subtraction) rule, you start with the operation inside the parenthesis. However, because it only involves one operation, which is addition, the order does not matter because of the Commutative Property of Addition.

What are the factors for 31

Answers

31 is prime meaning that its only factors are 1 and itself.

Final answer: 1, 31

31 is not even it is an odd number

So it will be 1 & 31

1x31=31

A six-sided number cube labeled 1 through 6 is rolled 600 times. An odd number is rolled 272 times. Compare the experimental probability of rolling an odd number with the relative frequency of rolling an odd number and select one of the statements below that best describes the situation.

Answers

1) Experimental probability: = (number of favorable outcome)/(number of trial:
= 272/600 = 0.4533.

2) Relative frequency = number rolls/Total number of rolls = 272/600

1) is the same as 2)

Answer:

Experimental probability and relative frequency are the same

Step-by-step explanation:

PLEASE HELP!

The graph below shows the height an elevator travels, y, in x seconds:

A graph is shown with x axis title as Time in seconds. The title on the y-axis is Height of Elevator Above Ground in feet. The values on the x-axis are from 0 to 5 in increments of 1 for each grid line. The values on the y-axis are from 0 to 125 in increments of 25 for each grid line. A line is shown connecting points on ordered pair 1, 25 and 2, 50 and 3, 75 and 4, 100. The title of the graph is Rate of Ascent.

What is the rate of change for the relationship represented in the graph?

50
25
fraction 1 over 25
fraction 1 over 50

Answers

The graph is not given , but with the help of information provided by you in the question:

X : 0 1 2 3 4 5 →→ Time in Seconds

Y : 0 25 50 75 100 125 →→Height of Elevator Above Ground in feet

Rate of change can be found by using two point slope form of line.

The slope of line joining two points [tex](x_{1},y_{1}) and (x_{2},y_{2})[/tex] is given by = [tex]\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]

Taking two points (1,25) and (2,50) and finding the slope of line, that is Rate of change:

Rate of change = [tex]\frac{50-25}{2-1}=25[/tex]

Option (B) 25 is correct answer.

5 divided 1 squared plus 1

Answers

6 because 5 divided by 0ne squared is 5 and + 1 is 6

Answer: 6

Step-by-step explanation: Use a calculated bro

Which expression represents the value, in dollars, of a certain number of dimes, d, and nickels, n? 0.10d + 0.05n 0.05d + 0.10n 0.15d + n 0.15dn

Answers

0.10d+0.05n because a nickel is .05 of a dollar and a dime is .10 of a dollar so you multiply d by.10 and add that by .05 times n to get what part of a dollar is d dimes and n nickels.

Answer:

0.10d+0.05n

Step-by-step explanation:

Simplify open parentheses x to the 5 eighths power close parentheses to the 2 thirds power.

Answers

If we are to express the word problem to its mathematical expression,

(x^5/8)^2/3

The concept to be used in order to answer this item is the product of the exponents. If,

(x^m)^n

The final answer would be,

x^mn

If we apply the same principle to the equation above,

(x^5/8)^(2/3)
x^(5/8)(2/3)
x^5/12
Thus, the most simplified form is equal to x^5/12.

Answer:

[tex]x^{\frac{5}{12}}[/tex]

Step-by-step explanation:

[tex](x^{\frac{5}{8}})^{\frac{2}{3}}[/tex]

To simplify it we multiply the exponents inside with exponent outside

[tex](a^m)^n = a^{mn}[/tex]

[tex]\frac{5}{8} *\frac{2}{3}[/tex]

Cancel out 8 and 2

[tex]\frac{5}{4} *\frac{1}{3}[/tex]

[tex]\frac{5}{12}[/tex]

tex](x^{\frac{5}{8}})^{\frac{2}{3}}=\frac{5}{12}[/tex]

x varies directly as y, and x = 153 when y = 9. Find x when y = 13.

Answers

153/9 = x/13

153 x 13 = 1989

1989/9=221

x = 221

y = kx
9 = 153k
k = 9/153
k = 3/51

so if y = 13 then
13 = 3/51 x
x = 13 (51/3)
x = 221

answer
x = 221 when y = 13.

there is two boxes to fill out

Answers

For the first pattern, the pattern is add 2, then 3, 4, 5, and so on.
1+2=3, 3+3=6, 6+4=10, 10+5= 15
For the second pattern, you multiply by 3 each time.
1*3=3, 3*3=9, 9*3=27, 27*3= 81
Final answers: 15 for first sequence, 81 for second sequence

write an integer for the situation below : 13 feet below the sea level

Answers

It is -13. It is below so negitive

At sea level we would be at 0 feet above the sea. If we are 13 feet below the sea level then we are 0 - 13 or -13 feet below the sea.

So, -13 feet is the answer.

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