Mathematics High School

The sum of the first (n) terms of the sequence is given by the formula (given below) . If this sequence is a geometric progression, find q. If this sequence is an Arithmetic progression, find d​

The Sum Of The First (n) Terms Of The Sequence Is Given By The Formula (given Below) . If This Sequence

Answers

Answer 1

Answer:

We have established the following sequence

6, 12, 18,...

The given is the Arithmetic sequence with the nth term

[tex]a_n=6n[/tex]

d = 6 is a common difference.

Step-by-step explanation:

Given the formula

Sₙ = 3n² + 3n

Put n = 1 to determine the sum of the first term

S₁ = 3(1)² + 3(1)

S₁ = 3 + 3

S₁ = 6

As the sum of the first term includes the only first term, so

a₁ = 6

Put n = 2 to determine the sum of the two terms

Sₙ = 3n² + 3n

S₂ = 3n² + 3n

S₂ = 3(2)² + 3(2)

S₂ = 12 + 6

S₂ = 18

as

S₂ = a₁ + a₂

substituting S₂ = 18, a₁ = 6

18 = 6 + a₂

12 = a₂

so

a₂ = 12

Put n = 3 to determine the sum of the two terms

Sₙ = 3n² + 3n

S₃ = 3(3)² + 3(3)

S₃ = 27 + 9

S₃ =36

as

S₃ = a₁ + a₂ + a₃

substitutingS₃ =36, a₁ = 6, a₂ = 12

36 = 6+12+a₃

a₃ = 36-6-12

a₃ = 18

Thus,

a₁ = 6

a₂ = 12

a₃ = 18

Therefore, the sequence becomes

a₁, a₂, a₃,...

6, 12, 18,...

Let us check the common difference 'd' between the adjacent terms

d = 12 - 6 = 6

d = 18 - 12 = 6

As the common difference 'd' between adjacent terms is the same, therefore the sequence is Arithmetic.

Thus,

d = 6

Furthermore, the nth term of the Arithmetic sequence can be defined as

[tex]a_n=a_1+\left(n-1\right)d[/tex]

substituting d = 6 and a₁ = 6

[tex]a_n=6\left(n-1\right)+6[/tex]

[tex]a_n=6n[/tex]

Related Questions

Question 2. Mode is the
(a) middle most frequent
value
(b) least frequent value
(c) maximum frequent value
(d) none of these​

Answers

A... mode is the value that appears the most.

Mr. Jacobs wants to save over $3,400 for a car. He has a savings account balance of $800 and will make equal weekly deposits for the next 25 weeks.

How much money should Mr. Jacobs deposit each week?

Answers

Answer:

64$

Step-by-step explanation:

Mr. jacobs should deposit $104 a week

The number of oranges purchased varies directly as the price of the oranges. If 11 oranges cost $2.35, what is the cost of 18 oranges?

Answers

Your Answer—- $3.85

Question 10
Which of the choices below is an irrational number?

Answers

Answer:

it is C  (squr. root 18)

Step-by-step explanation:

Answer:

c

Step-by-step explanation:

√18 because is not a perfect square or you can write it as a fraction

helpppppp plssssssss

Answers

Answer:

d

Step-by-step explanation:

I THINK

Find the slope between the two points.
(2,7) and (5, 8 )

Answers

Answer:

Slope

0.33

Step-by-step explanation:

Order the set of integers from greatest to least. {-100, -89, -124, -69, -52}

Answers

Answer:

-52, -69, -89, -100, -124

Step-by-step explanation:

When your dealing with negative numbers the smaller number the larger it is.

Hope this helps have a nice day:)

Steph needs to help her parents put a fence around their pool. They want the fence to be square and want each side to measure 6 meters. They already have 10 meters of fencing.
How many more meters of fencing should they buy?

Answers

Answer:a

Step-by-step explanation:

a

Jerry borrowed $400 for 5 years at 6% simple interest rate. What will the value of Jerry’s account be after 5 years

Answers

Answer:

here's the answers...,........

Find the value of x in the triangle shown below

Chose 1 answer

A. x = 2

B. x = 5

C. x = square root of 5

D. x = square root of 17

Answers

Answer:d

Step-by-step explanation:

Answer:

i think d

Step-by-step explanation:

it seems right

Solve the compound inequality n+2≤−5 and n+6≥−6 .

Answers

−
12
≤
n
≤
−
7
Explanation:
we solve each inequality separately, n then combine to get the final answer. :)
n
+
2
≤
−
5

n
≤
−
5
−
2

n
≤
−
7
n
+
6
≥
−
6

n
≥
−
6
−
6

n
≥
−
12
therefore combining the inequalities,
n
≤
−
7
and
n
≥
−
12
−
12
≤
n
≤
−
7

12 men can dig a pond in 8 days. How many men can dig it in 6 days?

Answers

Answer:

It would be 16 men.

Step-by-step explanation:

Let the number of men dig a pond in 6 day be x. Then,

It is a case of inverse variation.

12 × 8 = 6x

=> 96 = 6x

=> x = 96/6

=> x = 16

Hence, 16 men can dig a pond in 6 days.

Answer:

Answer is 16…..

12 men take 8 days for digging a pond, so we use simple method to solve this problem.

We multiple the both things that is 12 and 8 then get 96 is the result which is equal to multiple of 6 days and ?Men then get 16 men

Step-by-step explanation:

I literally put it on the comments lol

Which line has a slope of 1/2 and passes through (2,-4) ?

Answers

I believe graph C. (Bottom left)
Since it’s positive slope and goes through quadrant 1


If a temperature is 2 °C and falls by 7 °C, what is the new temperature?

Answers

Answer:

-5 degrees C

2 degrees C  minus 7 degrees C

hope this helps you

Solve the system of equations 4x + y = 8 and 5x + 2y = 13 using any method.

Answers

Answer:

x=1, y=4 or (1,4)

Step-by-step explanation:

Step-by-step explanation:

4x + y = 8

-4x -4x

y = -4x+8

5x + 2y = 13

-5x -5x

2y/2 = -5x/2 + 13/2

y = -5/2x+13/2

Using interval notation, the domain off is [- 3, 5] and the domain of g is [- 2, 7] . On what domain is f defined

Answers

Note: I am assuming you mean ''on what domain is f+g is defined''.

Answer:

We conclude that

Dom(f+g) = [-2, 5]

Step-by-step explanation:

Given the domain of f

[-3, 5]

Given the domain of g

[-2, 7]

The domain of a composition f+g would include the intersection of both domains.

In other words, the domain of a composition f+g includes all the inputs of x-values that are in the domain of both functions i.e. f and g.

so

Domain of f = [-3, 5]

The x-values lie in the domain of f interval are:

x = -3, -2, 1, 0, 1, 2, 3, 4, 5

Domain of g = [-2, 7]

The x-values lie in the domain of g interval are:

x = -2, 1, 0, 1, 2, 3, 4, 5, 6, 7

Therefore, the common x-values in both f and g would be:

-2, 1, 0, 1, 2, 3, 4, 5

Thus, we conclude that

Dom(f+g) = [-2, 5]

Offering 100 Points for someone to complete the worksheet.

Answers

Answer:

what is the question?

please post the question

estimate of 2728/124​

Answers

Answer: the real answer is 22 but a way for you to get a good estimate would be too look at the equation as 2730/120 and then you would get 22.75.

Step-by-step explanation:

Answer: the real answer is 22 but a way for you to get a good estimate would be too look at the equation as 2730/120 and then you would get 22.75.

Step-by-step explanation:

factorise the following
a) 32a^2-98b^2
b)m ^2 -64n^2

Answers

Answer:

a) 2(4a + 7b)(4a - 7b)

b) (m - 8n)(m + 8n)

Step-by-step explanation:

[tex]a)32a^{2} - 98b^{2}\\=(2 * 16)a^{2} - (2*49)b^{2}\\=2(16a^{2} -49b^{2})\\=2 ([4a]^{2}-[7b]^{2})\\=2(4a+7b)(4a-7b)[/tex]

[tex]b) m^{2} - 64n^{2}\\= (m)^{2} - (8n)^{2} \\= (m-8n)(m+8n)[/tex]

happy to help:)

Gabby spents $44.10 for 14 gallons of gas.what was the unit cost or price per gallon

Answers

Answer:

The unit cost is $3.15

Step-by-step explanation:

Here, we want to get the price per gallon

mathematically, that will be total amount spent divided by the number of gallons

That will be;

44.10/14 = $3.15

( Which of the following best describes an ecosystem in a neighborhood garden?

Answers

What are the answers for the nonshelaunt question

The sum of the digits of a two digit number is 10. If 36 is subtracted from the number, the digit interchange their places Find the number​

Answers

Step-by-step explanation:

Let A be the tens digit of the number and B be the ones digit.

We have A + B = 10 and 10A + B - 36 = 10B + A.

=> A + B = 10 and 9A - 36 = 9B

=> A + B = 10 and A - 4 = B

=> A + B = 10 and A - B = 4

Therefore 2A = 10 + 4 = 14,

A = 7 and B = 10 - 7 = 3.

Hence the number is 73.

Write an inequality for the graph below

Answers

Answer:

y ≤ -4x - 3

Step-by-step explanation:

First identify the line itself by using point slope [y - y1 = m(x - x1) ] given two points or find the slope by finding the rise of the line over the run [m = ∆y/∆x ] [∆ = change/difference]. Because you are already given the y-intercept, using the form y = mx + b, the y-intercept is -3 because that is where the line intersects the y axis or where x = 0 so b = -3.

Now from -3, you can tell that when you go 1 across, the line goes down 4 units so the slope or m must be -4. Because it goes from -3 to -7, that is a change of -4. This means the line is y = -4x - 3.

Because there is a solid line, and a shade (thought of as the y value) under the line, you will replace = [equal sign] with the ≤ [less than or equal sign]. Therefore the answer is y ≤ -4x - 3

15 is what % of 60:(

Answers

Answer:

25%

Step-by-step explanation:

What the answer is for this question

Answers

Answer:

im pretty sure its 24

Step-by-step explanation:

because 12+12=24

18. The length of the minor arc AB of a circle,
centre 0, is 27 cm and the length of the major
arc is 221 cm. Find (a) the radius of the circle,
(b) the acute angle AOB.​

Answers

Hope this might help u

How do i solve
X^56 x X^14

Answers

Answer:

x^70

Step-by-step explanation:

When multiplying exponents, you just add them up.

x^56+14= x^70

Coca Cola is offering prizes under the caps of their sodas. Coca Cola claims that “one in six game pieces wins a prize.” The official rules of the contest states that the odds of winning a prize are 1:6. Is the claim “one in six game pieces wins a prize” correct? Why or why not?

Answers

Answer:

correct because one in six game pieces win a prize.

Step-by-step explanation:

ASAP PLEASE HELP ME

Answers

Answer:

6 would be opposite

Step-by-step explanation:

Consider the conditional statement:
"If the store has the Playstation 5 in stock, then I will buy one."
What is the conclusion of the statement?

Answers

Answer:

he's getting the ps5

Step-by-step explanation:

In conclusion if the store has the ps5 he's getting it and if not he wont

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