sum of the first nth term of a series is given by Sn = n (3n-4). Show that the terms of the series are in arithmetic progression​

Answers

Answer 1

Answer:

see explanation

Step-by-step explanation:

Using the sum to n terms formula, then

S₁ = 1(3 - 4) = 1(- 1) = - 1 ⇒ a₁ = - 1

S₂ = 2(6 - 4) = 2(2) = 4, then

a₂ = S₂ - S₁ = 4 - (- 1) = 4 + 1 = 5

S₃ = 3(9 - 4) = 3(5) = 15, then

a₃ = S₃ - S₂ = 15 - 4 = 11

S₄ = 4(12 - 4) = 4(8) = 32 , then

a₄ = S₄ - S₃ = 32 - 15 = 17

S₅ = 5(15 - 4) = 5(11) = 55 , then

a₅ = S₅ - S₄ = 55 - 32 = 23

The first 5 terns of the series are

- 1, 5, 11, 17, 23

There is a common difference (d) between consecutive terms

d = 5 - (- 1) = 11 - 5 = 17 - 11 = 23 - 17 = 6

Thus the series is in arithmetic progression


Related Questions

What is the value of x?
Enter your answer in the box.

x = ___

Answers

The value of x from the given diagram using the similarity theorem of a triangle is 7

In order to get the value of x from the given triangle, we will use the similarity theorem of a triangle.

From the given triangle, the following equation is true;

5/40 = 3/2x + 10

Cross mutiply

5(2x + 10) = 3(40)

10x + 50 = 120

10x = 120 - 50

10x = 70

x = 7

Hence the value of x from the given diagram is 7

Learn more here: https://brainly.com/question/23961310

Olivia is thinking of a number. she says, "my number is odd. It is a factor of 30 and a multiple of 3" There are two numbers she is thinking of, what are those numbers?

Answers

Answer: The answer is 15


Explanation: 3 can go into 15

i have no clue what im doing.. please help​

Answers

Answer:

2

Step-by-step explanation:

If triangles are similar (like shape ratios are exactly the same), then, 21 ÷ 3 = 7.  Now you know the ratio to apply.  So, side with the length of 14 s/b divided by that ratio of 7, that is, 14 ÷ 7 = 2

eishdjjsdjjxjxididhdjxix

Answers

42 (divide 256/6 and you get 42.6666 but you can only fill 42 completely, not 43 cuz one would be only 60% filled)
42 just divide 256 by 6

In a physics lab, an artifact is dropped from the roof of the school building, 98 feet above the ground. The height ݄ (in feet) of the ball above the ground is given by the function h(t)=-16t^2+98, where t is the time in seconds.

Answers

Answer:

The algebraic expression h = 16 feet.

Ali receives a 4% commission for all his sales. His sales for January were $15,000. What was the commission amount he earned for the month of January?

Answers

Answer:

$600

Step-by-step explanation:

Convert the 4% commission into a decimal, which is 0.04.Multiply the sales ($15,000) by the commission as a decimal (0.04). This is $600, which is the answer.

Can someone plzzz help ASAP

Answers

Answer:

x = 7 √3 km

Step-by-step explanation:

Here, we want to get the value of x

As we can see, we have a right angled triangle with hypotenuse 14 km

we can use the Pythagoras’ theorem to get the value of x

Mathematically, the square of the hypotenuse equals the sum of the squares of the two other sides

Thus,

14^2 = x^2 + 7^2

x^2 = 196-49

x^2 = 147

x = 7 √3 km

BE NICE AND SOLVE PLS

Answers

Answer:

BC=FE=5

BC=5

BA=DE=11

angle A= angle D=27

whitch of the functions below could have created this graph

Answers

Answer:

C

Step-by-step explanation:

2 roots: 1 , -1

f(1) = 0 and f(-1) = 0   only function C fit the condition

A parking lot has 7 red cars out of a total of 35 cars. What percent of the cars in the parking lot are red? Enter your answer in the box.​

Answers

Answer:

20%

Step-by-step explanation:

Answer:

% of Red CARS = 20%

Step-by-step explanation:

Total CARS = 35

Red CARS = 7

% of Red CARS = (red cars ÷ total cars)*100

% of Red CARS = (7÷35)*100

% of Red CARS = 20

Which statement is correct?
O A.
The opposite of the opposite of 6 is 6.
OB.
The opposite of the opposite of 1 is 1.
O C.
The opposite of the opposite of 3 is 0.
O D.
The opposite of the opposite of 5 is.

Answers

Answer:

I think its OB but I'm not sure

Step-by-step explanation:

What is the area of triangle ABC? a \large 6\sqrt{3} square units b \large 18\sqrt{3} square units c \large 36\sqrt{3} square units d \large 72\sqrt{3} square units

Answers

question isn't clear but I believe you are asking for the area of triangle ABC given sides a, b, c

We use the example question:

Find the area (in square units) of the triangle described.

a = 49mm, b = 33mm, c = 18mm

Answer and explanation:

We apply Heron's formula to solve the area of a triangle given the sides of the triangle a, b, c

A= √s(s-a)(s-b)(s-c)

Where A = area of triangle in square units

s= semiperimeter(a+b+c/2) of a triangle

a, b, c= lengths of the sides of the triangle

Therefore area of triangle =√50(50-49)(50-33)(50-18)

= √27200

=164.92mm²

Find 27.1% of 208. Round to the nearest tenth.

Answers

Answer:

56.4 is your answer

Correct me if I'm wrong.

Answer:

56.368

Step-by-step explanation:

the cos c of recycle Tin can varies directly as it's weight w in kilograms .if a junk shop pays 60 pesos per kilo of tin cans how many kilos should a junk shop pay an amount of 390 pesos​

Answers

Answer:

Step-by-step explanation:

c = 60w

390 = 60w

w = 6.5 kilograms

When 20 large rooms are occupied, the total amount of money collected from the large room is $1800. When 10 large rooms and 21 small rooms are occupied, the hotel collects $2370. How much does the hotel charge for each small room?

PLEASE I NEED HELP ITS DUE TODAY!

Answers

It is 70
i cant explain it right now i have work to do so sorry:)
Large room price:
20L = 1800
L = 90

10L + 21S = 2370

Then substitute what you know L is and solve for S (small room cost)
10(90) + 21 S = 2370
900 + 21 S = 2370
21S = 1470
S = 70

A coffee can in the shape of a cylinder has a Volume of V = 67.57 in. Find the forumla that gives the radius of the coffee can, r, in terms of the volume V and height h. If the height is 7.5 inches, what is the radius of the coffee can?​

Answers

Answer:

r = sq rt [v/(h x Pi)]

r = 1.69

Step-by-step explanation:

v=h x Pi x r^2

r^2 = v/(h x Pi)

r = sq rt [v/(h x Pi)]

r = sq rt [67.57 / (7.5 x 3.14)]

r = sq rt 2.8692

r = 1.69

Help my friendddddddddddd

Answers

Hey ur literally owowowo I can’t stop

Answer:

It would be a positive correlation

Step-by-step explanation:

Please Help Me!!!
Andre is making paper cranes to decorate for a party. He plans to make one large paper crane for a centerpiece and several smaller paper cranes to put around the table. It takes Andre 10 minutes to make the centerpiece and 3 minutes to make each small crane. He will only have 30 minutes to make the paper cranes once he gets home.
​Andre wrote the inequality 3x + 10 ≤ 30 to plan his time. Describe what x, 3x, 10, and 30 represent in this inequality.
Solve Andre’s inequality and explain what the solution means.

Answers

Answer:

6 small cranes

Step-by-step explanation:

3x + 10 is less than or equal to 30

3 is the minutes for the small cranes

X is the amount of small cranes

10 is the minutes for the large crane

30 is the total time limit

first, subtract 10 from 30, which gives you 20 so

3x is less than or equal to 20.

to figure this out, divide 20 by 3, which gives you 6 with a remainder of two minutes.

Andre can make 6 small cranes.

Consider the relationship in special right triangles to determine the tangent ratio for a 45 degree angle. Give your answer, as necessary, to the nearest thousandth place (three decimal place values).

Answers

Answer:

1

Step-by-step explanation:

The tangent of a angle is opposite side/ adjacent side

In a rights triangle with a 45° angle we have a special 45-45-90 triangle.

The legs of the triangle are congruent and are the opposite and adjacent sides of the 45° angle.  Therefore, the ratio of those two sides is 1.

Therefore, the tangent of 45° = 1

10x -20 plus 7x plus 4 equals 180 what is x

Answers

Answer:

x is approximately 11.5

Explanation:

10x - 20 + 7x + 4 = 180

17x - 16 = 180

17x = 196

x is approximately 11.5

i need help with number 5

Answers

Answer:

the graph is not exponential because exponential is represented as a form of exponenti growth or exponential decay. Exponential function has a slight curve rather than a straight line

The person above me is right^^

Sarah has 30 oranges an 48 plums . What is the ratio of oranges to plums

Answers

Answer:

30:48

Step-by-step explanation:

because there are 30 oranges and 48 plums. I got this by putting oranges in front of plums to get the ratio of 30:48

Please help I’ll give you brainleast and thanks

Answers

Answer:

i got 49

i think its correct

Step-by-step explanation:

All angles in a triangle must add up to 180. So 90+49+?=180 in order to find the. Mystery number we add 90+49 to get 139. And then we figure out what number plus 139 equals 180 . That number would be 31

Ryan ordered some books online and spent a total of . Each book cost and he paid a total of for shipping. How many books did he buy?

Answers

Answer: 12 books

Step-by-step explanation:

First you need to remove the cost of shipping from the total amount:

= 75 - 3

= $72

The above is the total amount spent on the books without shipping.

If each book cost $6, the total number of books bought is:

= 72 / 6

= 12 books

Solve: -8(x - 3y - 9)
Your answer

Answers

-8x + 24y + 72

————————-

Answer: −8x+24y+72

-8(x - 3y - 9)

=(-8)(x + -3y + -9)

=(−8)(x)+(−8)(−3y)+(−8)(−9)

=−8x+24y+72

Step-by-step explanation:

im not entirely sure but i hope this helps

:) have a nice day !!

-29=9-6k-2k - 1please do the work, i’ll mark as brainliest

Answers

Answer:

k = 37/8

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right  

Equality Properties

Multiplication Property of Equality Division Property of Equality Addition Property of Equality Subtraction Property of Equality

Algebra I

Terms/Coefficients

Step-by-step explanation:

Step 1: Define

-29 = 9 - 6k - 2k - 1

Step 2: Solve for k

Combine like terms:                                                                                       -29 = 8 - 8k[Subtraction Property of Equality] Subtract 8 on both sides:                      -37 = -8k[Division Property of Equality] Divide -8 on both sides:                              37/8 = kRewrite/Rearrange:                                                                                        k = 37/8

Step 3: Check

Plug in k into the original equation to verify it's a solution.

Substitute in k:                                                                                                -29 = 9 - 6(37/8) - 2(37/8) - 1Multiply:                                                                                                           -29 = 9 - 111/4 - 37/4 - 1Subtract:                                                                                                          -29 = -75/4 - 37/4 - 1Subtract:                                                                                                          -29 = -28 - 1Subtract:                                                                                                          -29 = -29

Here we see that -29 does indeed equal -29.

∴ k = 37/8 is the solution to the equation.

About 8 out of 15 homes have a
dog as a pet. On a street with 165
homes, how many would you
expect to have a dog for pets?
with dogs

Answers

i believe 88 homes have pets

If each of the two equations shown below are graphed in the same xy-coordinate plane, the graphs intersect. What is the x -coordinate of one of these points of intersection? y = 2x−9 y=−(x−1)2−7

Answers

Answer:

The graphs do intersect at two values of x;

x = 1

and

x = -1

Step-by-step explanation:

We have the two equations:

y = 2*x - 9

y = -(x - 1)^2 - 7

We know that when we graph these equations, the graphs do intersect.

if the graphs intersect, then we must have at least one point (x, y) that is a solution for both equations.

because in this point y is the same for both equations, then we can write:

2*x - 9 = y = -(x - 1)^2 - 7

this leads to the equation:

2*x - 9 = -(x - 1)^2 - 7

now we can solve this for x.

2*x - 9 + (x - 1)^2 + 7 = 0

2*x + x^2 - 2*x + 1 + 7 - 9 = 0

x^2 - 1 = 0

x^2 = 1

x = √1

Then we have two possible solutions:

x = 1, and x = -1

Does anyone under stand this one ??

Answers

Answer:

its c i belive'

Step-by-step explanation:

solve for N
what's the rule

Answers

Answer:

n = 8

Step-by-step explanation:

The rule for this table is multiply x by 4 to get y. To solve for n, divide y (32) by 4 to get x (8).

Hope it helps!

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