Find the explicit formula for the n​th term of the following sequence where the first term is a1
{-6/7, 7/9, -8/11, 9/13, -10/15, ...}

Pls no links, I actually need help

Find The Explicit Formula For The Nth Term Of The Following Sequence Where The First Term Is A1{-6/7,

Answers

Answer 1

The numerators in each term are consecutive integers ≥ 6. If n = 1 refers to the first term, then the numerator of the n-th term would be n + 5.

The denominators are consecutive odd integers ≥ 7. Odd numbers take the form 2k - 1, where k is any integer, and 2k - 1 = 7 when k = 4. But we want our sequence to start at n = 1, so we replace k here with n + 3. Then the denominator of the n-th term would be 2 (n + 3) - 1, or 2n + 5.

The odd-indexed terms are negative, while the even-indexed terms are positive. We can account for the sign of the term by multiplying by (-1)ⁿ.

Taking everything together, it follows that the n-th term in the sequence is

[tex]a_n = (-1)^n \dfrac{n + 5}{2n+5}[/tex]


Related Questions

Write the quadratic equation whose roots are 1 and -2, and whose leading coefficient is 3.
(Use the letter x to represent the variable.)
I = 0
х
5
?
Save For Later
Su
Check
2021 Mc LLC All Rights Reserved tesof Use Peso
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Answers

Answer:

See below

Step-by-step explanation:

The quadratic equation in factored form:

a(x - α)(x - β), where a- leading coefficient, α and β - roots

We have:

a = 3, α = 1, β = -2

Substitute them to get:

3(x - 1)(x + 2)

Converting this into standard form:

3(x - 1)(x + 2) =3(x² + x - 2) =3x² + 3x - 6

How do u Keep change change this number???

1.3 - -300=????

I don’t know what to do

Answers

1 .3 - -300
1.3 + 300
301.3

Which of the following statements is the only
sentence that is error-free?

Answers

I don’t really know what the answer is

x=4y,2x+y=18 solve by substitution show all work

Answers

Here is the math, did it on paper, sorry it’s blue. just add parenthesis around the x in the second equation and add what x equals. then solve as PEMDAS.

Shelby will take a total of 6 tests. On the first 5 tests, her scores were: 80, 85, 73, 78, 90. If she wants a mean grade of 80, what does Shelby have to score on her 6th test?

84
80
90
74

Answers

Answer:

74

Step-by-step explanation:

The mean of any set of numbers is simply the sum of the numbers divided by however many numbers you have. Because of this you can write the following equation

Mean = (sum of numbers)/(number of numbers)

Let's say that the missing test score is called x:

Mean = 80 = (80 + 85 + 73 + 78 + 90 + x)/6

80(6) = 80 + 85 + 73 + 78 + 90 + x

480 = 80 + 85 + 73 + 78 + 90 + x

x = 480 - 80 - 85 - 73 - 78 - 90

x = 74

What is the domain and range of the function f(x)=17?

Answers

D: All Real Numbers R: [17,17]
First, rewrite as y=17. This will look like a horizontal line.

Domain is all x values represented. If the line is infinately horizontal, the domain is all real numbers

Range is all y values. The only y value is 17. So u can write range as y=17. I don’t know what the other dude was doin with brackets. It’s simply y=17

Is -4/19 equivalent to 4/-19

Answers

Answer:

Yes.

Step-by-step explanation:

Answer:

no.

Step-by-step explanation:

-4/19 is completely different to 4/-19.

Im not sure how to word it but they are two completely different numbers.

i need help on this asap

Answers

Answer:

c

Step-by-step explanation:

divide x² +x +1 by x+ 1 by long division method​

Answers

Answer:

I hope it will help you.

Paul left his house at 9:45 a.m. and returned home at 6:55 p.m. the same day. How long was Paul away from home?

Answers

Answer:

9 hours and 10 minutes

Resultado de la operación -2-(5-3)+4

Answers

Answer:

0

Step-by-step explanation:

-2-(5-3)+4

-2-2+4

-4+4

0

Answer this pleaseeee <3 <3 <3 <3 <3 <3 <3

Answers

Answer:180%

Step-by-step explanation:

72/40 = 1.8

(1.8)(100)= 180

Answer:

Answer: 180%

Step-by-step explanation:

please help me write an expression for area and perimeter for this rectangle ​

Answers

[tex]\text{Given that ,}\\\\\text{Length,}~ l = (2y+5)~\text{units.}\\\\\text{Width, } w= 3~\text{units.}\\\\\\\text{Area} = lw = (2y+5)(3) = (6y+15) ~~ \text{units}^2.\\\\\\\text{Perimeter} =2(l+w) = 2(2y+5 +3) = 2(2y+8) = (4y+16)~~ \text{units}.[/tex]

Find s(16) for the sequence s(n)=4n-2, ne {1, 2, 3, ... }.
A
64
B
60
66
D
62

Answers

Answer:

62

Step-by-step explanation:

Substitute n = 16 into the sequence rule

s(16) = 4(16) - 2 = 64 - 2 = 62

A ___ equation is a second-degree equation of the form ax^2+bx+c=0 where a ≠ 0​

Answers

Answer:

A quadratic equation is second degree equation with the standard form ax^2+bx+c=0 as the highest power is 2.

__________________.

PLZ HELP
Use the distributive property to remove the parentheses.​

Answers

Answer:

I don't know if i did this correctly because i can't find my notes but i hoped i helped.

Step-by-step explanation:

pls help!! the answers are written but can someone explain how to find the angles step by step? I already know how to find the hypotenuse length.

Answers

There are a few options we can take. One way is to use the tangent ratio to tie together the opposite and adjacent sides, and then apply the inverse tangent (aka arctangent) to get the angle itself.

Let x be the upper left acute angle, and y be the lower right acute angle.

We can say

tan(angle) = opposite/adjacent

tan(x) = 16/5

x = arctan(16/5)

x = 72.645975 approximately

x = 72.6

and also

tan(angle) = opposite/adjacent

tan(y) = 5/16

y = arctan(5/16)

y = 17.3540246

y = 17.4

Note how x+y = 72.6+17.4 = 90. The two acute angles of any right triangle are complementary, meaning they always add to 90. So if you found x, then you can compute y = 90-x without needing the tangent ratio.

Your calculator needs to be in degree mode when using the arctangent function, which is denoted as [tex]\tan^{-1}[/tex] on many graphing calculators.

Rachael is placing a protective cover on a glass case. The case is a cube, and the perimeter of one cube face is 56 inches.

How many square inches of the protective covering does she need for the case?

Answers

Answer:

336

Step-by-step explanation:

We know that a cube has 6 faces which means we can use this equation:

56 x 6 = 336

336 square inches is the answer.

Perimeter=56in

Side=56)4=14in

So area of one side=

(side)^2=(14)^2=196in^2

Cube has 6sides

So total protection:-

6(196)1176in^2

Can someone help me ? :

Answers

Answer:

[tex]\huge\boxed{\sf y = 100.4}[/tex]

Step-by-step explanation:

Given equation is:

53 = y - 47.4

Add 47.4 to both sides

53 + 47.4 = y

100.4 = y

OR

y = 100.4

[tex]\rule[225]{225}{2}[/tex]

Hope this helped!

~AH1807

Hello there!

Question:-

[tex]\sf \longmapsto53=y - 47.4[/tex]

This is a equation. We need to find the value of variable y.

Solution:-

[tex]\sf \longmapsto53=y- 47.4[/tex]

To Solve further,we need to overturn the equation.

That is :-

[tex]\sf \longmapsto \: y - 47.4 = 53[/tex]

Then, Add +47.4 to two sides:-

[tex]\sf \longmapsto \: y - 47.4 + 47.4 = 53 + 47.4[/tex]

On Simplification:-

Note that (-) and (+) equals to (-). So it would be 47.4 - 47.4 . Which results to 0.

[tex]\sf \longmapsto \: y - 0 = 100.4[/tex]

[tex]\sf \longmapsto \: y = 100.4( Ans.)[/tex]

Answer as a mixed fraction:-

[tex]\sf \longmapsto 100\dfrac{2}{5}[/tex]

Answer as a fraction:-

[tex]\sf\longmapsto 502/5[/tex]

______________________________________

Henceforth, the value of y is :-

[tex]\bf \: y = 100.4[/tex]

Or as a mixed fraction:-

[tex]\bf y = 100\dfrac{2}{5}[/tex]

Or as a fraction:-

[tex]\bf y = 502/5[/tex]

________________________________

I hope this helps!

Please let me know if you have any questions.

3. Solve each equality or inequality:
a. |8x-6|= 0

Answers

Answer:

x = 3/4

Step-by-step explanation:

Step 1: Find possibilities.

We know one possibility: 8x - 6 = 0. This is because 0 cannot be positive or negative.

Step 2: Solve possibility 1.

[tex]8x - 6 = 0[/tex] [tex]8x - 6 + 6 = 0 + 6[/tex] (Add 6 to both sides)[tex]8x = 6[/tex] [tex]\frac{8x}{8} =\frac{6}{8}[/tex] (Divide both sides by 8)[tex]x = \frac{3}{4}[/tex]

Therefore, x = 3/4.

What is the factored form of n^3+512 (please answer) picture provided

Answers

[tex] {n}^{3} + 512 \\ = {(n)}^{3} + {(8)}^{3} \\ by \: using \: {a}^{3} + {b}^{3} = (a + b)( {a}^{2} - ab + {b}^{2}) we \: \: \: get \\ = (n + 8)( {(n)}^{2} - n \times 8 + {(8)}^{2} ) \\ = (n + 8)( {n}^{2} - 8n + 64)[/tex]

Hope you could get an idea from here.

Doubt clarification - use comment section.

solve the equation 3÷7x-1+1÷x=0​

Answers

Answer: The answer is 3x^2 - 7x + 7 = 0.

What percent is a gram of a kilogram

Answers

Answer:

0.1 percent

Step-by-step explanation:

What is the volume of a cone with the height of 6 inches and the diameter of 4 inches?
A) 25.20in3
B) 25.12in3
C) 26in3
D) 25in3
Will get brainliest

Answers

A is the answer because I had the answer on I ready

Please help me…………….

Answers

Answer:

Isosceles triangle.

Step-by-step explanation:

An online furniture store sells chairs and tables. Each day, the store can ship at most 55 pieces of furniture. Write an inequality that could represent the possible values for the number of tables sold, t, and the number of chairs sold, c, that would satisfy the constraint.

Answers

Answer:

t+c ≤ 55

Step-by-step explanation:

t+c is the total pieces of furniture and it must be at most (less than or equal to) 55 so t+c ≤ 55 is the equality that represents the possible values.

Q.The total surface area of a cylinder is
3080cm² and height is 21cm. Find its base radius.
Show full process.

Answers

Answer:

r≈14cm

h Height

21

cm

A Surface area

3080

cm²

Using the formula

A=2πrh+2πr2

Solving forr

r=1

2h2+2A

π﹣h

2=1

2·212+2·3080

π﹣21

2≈14.00402cm

30 POINTS John opens a savings account and decides to deposit $10 each month. Let x represent the number of
months that he has been saving, and y, represent the total amount of money saved.
7. What is the algebraic equation for John's saving plan?
8. How much money will John have saved in 14 months? In 6 months? Show your work and
explain.
9. In how many months will John have saved $100? $175? Show your work and explain.
10. What is the rate of change?
11. How does knowing the rate of change help you in answering questions in this problem?
12. Use your equation to complete the table representing John's savings:
# of Months Saving Account Balance ($)
0
1
2
3
4

Answers

Answer:

7.) y=10x

8.) $140 in 14 months, $60 in 6 months

9.) He will have saved $100 in 10 months and $175 in 17.5 months

10.) The rate of change is 10

11.) Knowing the rate of change helps you in answering this problem because it tells you how much money he saves per month.

12.)

0- $0

1- $10

2-$20

3-$30

4-$40

Step-by-step explanation:

7.) The standard form of a linear equation is y=mx+b

The starting balance is 0 so there is no point to adding b. M is the amount of money he deposits each month so that is 10. You plug in the values and you get y=10x (+0)

8.) y=10(14)

$140

y=10(6)

$60

9.) 100=10x

100/10= 10

10 months

175=10x

175/10=17.5

17.5 months

10.) The rate in change is m so 10.

Hope I explained this in simple enough terms. Have a good day!

2 people start from the same spot one walking east the other walking west, the person walking east walks slowly at 4mph and the other person walks fast at 6mph writr and solve a system of equations that can be used to determine how ong until 2 people are 2 1/2 miles apart from ach otherr

Answers

Answer:

3\5

Step-by-step explanation:

Katie works as a waitress and records her monthly tips in the table shown below. If Katie decided not to work the month of November, how would her five month average compare to her six month average for monthly tips? June July August Septemper October November $133. 45 $235. 31 $239. 45 $258. 87 $298. 45 $115. 67 a. Her monthly average would have decreased by $19. 57. B. Her monthly average would have increased by $19. 57. C. Her monthly average would have increased by $2. 7. D. Her monthly average would have decreased by $2. 7. Please select the best answer from the choices provided A B C D.

Answers

Her monthly average would have decreased by $19.57 and it can be determined by using taking the average value of every month.

Given that,

Katie works as a waitress and records her monthly tips in the table shown below.

June, July, August, September, October, November

$133.45, $235.31, $239.45, $258.87, $298.45, $115.67

If Katie decided not to work the month of November,

We have to determine,

How would her five-month average compare to her six-month average for monthly tips?

According to the question,

Katie works as a waitress and records her monthly tips in the table below.

June, July, August, September, October, November

$133.45, $235.31, $239.45, $258.87, $298.45, $115.67

To find out how not working in November would affect the average of Katie's tips.

The average of her working June until October only.

[tex]\rm Average = \dfrac{133.45 + 235.31 +239.45 + 258.87 + 298.45}{5}\\\\Average =\dfrac{ 1165.53 }{ 5}\\\\Average = 233.10[/tex]

Then, The average is with the month of November is,

[tex]\rm Average = \dfrac{133.45 + 235.31 +239.45 + 258.87 + 298.45 + 115.67}{6}\\\\Average =\dfrac{ 1281.2 }{ 6}\\\\Average = 213.53[/tex]

 

Therefore,

On comparing the average of her five-month average to her six-month average for monthly tips is,

[tex]233.10 - 213.53 = 19.57[/tex]

The average will decrease because 213.53 is less than 233.10.

Therefore, Her average will decrease by $19.57.

Hence, Her monthly average would have decreased by $19.57.

For more details about the Average value refer to the link given below.

https://brainly.com/question/8916264

Answer:

b

Step-by-step explanation:

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