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

ASAP PLEASE HELP ME

Answers

Answer:

6 would be opposite

Step-by-step explanation:

15 is what % of 60:(

Answers

Answer:

25%

Step-by-step explanation:

helpppppp plssssssss

Answers

Answer:

d

Step-by-step explanation:

I THINK

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

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

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 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

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

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

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

What the answer is for this question

Answers

Answer:

im pretty sure its 24

Step-by-step explanation:

because 12+12=24

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]

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

Answers

What are the answers for the nonshelaunt question

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

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

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.

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:


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

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...,........

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

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:)

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:)

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:

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

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

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

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

Offering 100 Points for someone to complete the worksheet.

Answers

Answer:

what is the question?

please post the question

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

Answers

Answer:

Slope

0.33

Step-by-step explanation:

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