8
The first term of an arithmetic sequence is 5. The third term of the sequence is 13.
Which of the following expressions represents the nth term of the sequence?
A 4n +1
B) 4n + 5
5n+1
D) 5n + 5

Answers

Answer 1

Answer:A 4n+1

Step-by-step explanation: found the answer key

Answer 2

If the first term of an arithmetic sequence is 5 and the third term of the sequence is 13 then the nth term is A) 4n +1.

What are arithmetic and geometric sequence?

An arithmetic sequence is a set of numbers in which every no. next to the previous number has the same common difference(d).

aₙ - aₙ₋₁ = aₙ₋₁ - aₙ ₋₂.

In a geometric sequence numbers are written in the same constant ratio(r).

It means every next number is a multiple of a common constant and the previous number.

aₙ/aₙ₋₁ = aₙ-₁/aₙ₋₂.

Given, The first term of an arithmetic sequence is 5.

The third term of the sequence is 13.

As we can conclude that for 2 terms the common difference is increased by 8.

∴ Common difference (d) = 8/2 = 4.

Now, we know the nth term of an arithmetic sequence is,

aₙ = a₁ + (n - 1).d.

aₙ = 5 + (n - 1)×4.

aₙ = 5 + 4n - 4.

aₙ = 4n + 1.

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Related Questions

I received $385 back from the government, which represented the 17.5% purchase tax on a piece of equipment. How much did I pay for this equipment in the first place?

Answers

Answer:

[tex]the \: equipment \: price \: is : 2,200.[/tex]

Step-by-step explanation:

[tex]let \: the \: original \: price \: be \: x \\ then \: 17.5\% \: of \: x = 385 \\ \frac{17.5}{100} \times x = 385 \\ 17.5x = 100 \times 385 \\ x = \frac{38500}{17.5} \\ x = 2,200.[/tex]

Does anyone know how to solve this 5x(x+4)^2-2y^5 x=-3 and y=-2

Answers

It’s 49.
5(-3)(-3+4)^2 -2(-2^5)
5(-3)x 1^2 +2^6
5(-3) x 1 +64
-15+64
=49

Answer:

49

Step-by-step explanation:

y = 9 - 1
What is this ?

Answers

y=8

your teacher is introducing algebra

Each year a store decreased the price of a certain model of TV by $35. If the
price in 2001 was $1,950, what was the price in 2009?
Group of answer choices

Answers

Answer:

dont you just multiply it should be 2,230

Step-by-step explanation:

It’s just 2,230i think sorry

Jennifer bought 4.25 pounds if chocolate covered pecans. If each pound of chocolate covered pecans cost $2.40 how much did Jennifer pay for the chocolate covered pecans?

Answers

Answer:10.2$

Step-by-step explanation:4.25 times 2.40=10.2

Answer:

4.25 * 2.40 = 10.2 pretty simple

Step-by-step explanation:

which equation matches the graph

A.y=2x+3
B.y=-2x+3
C.y=-4x+2
D.y=4x+2

Answers

The correct answer is A

Solve
(6x + 5) - (x + 3)

Answers

Answer:

5x+2

Step-by-step explanation:

6x-x=5x and 5-3=2

so 5x+2 is the answer.

Find the quadratic function.

Answers

The answer would be y=-6

Camelia misses 8 points on the first math test. She misses 5 points on the second math test. What integer represents the number of points Camelia misses on the first two test?

Answers

It’s the Equator so you divide it by 2

Please help me :( no ones helping me :( pls show how you got it too :( thank you ill give you all my points 30 points

Answers

Answer:

1. a. 110

because 5 less than 35 is 30 and 5 less than 10 is 5. it would only make sense for 5 less than 110 is 105

7. D. 54

every other number in the equation is one less (8,7,6,5)

and inbetween those the number is multiplied by 3 (2×3=6, 6×3=18) so then 18×3 =54

the middle left. D. 27

every other one is multiplied by 2 (2×2=4, 4×2=8, 8×2=16) but the first one is multiplied by 3. (1×3=3 3×3=9 9×3=27 27×3=81)

11. A.11

it adds 6 every other (17+6=23, 23+6=29)

for every other first one it adds 4. (7+4=11, 11+4=15, 15+4=19)

12. D. 18

for every other it adds 2.(4+2=6, 6+2=8)

for every other second it adds 6. (6+6=12, 12+6=18, 18+6=24)

15. D. 49

for every other it subtracts 6 (67-6=61, 61-6=55, 55-6=49)

the every other second it divides in half. (32÷2=16, 16÷2=8, 8÷2=4)

18. D. 17

for every other it adds 2.(13+2=15, 15+2=17, 17+2=19)

for every other second it subtracts 2. (21-2=19, 19-2=17, 17-2=15)

Step-by-step explanation:

im pretty sure these are correct, i hope this helps

A baking mix consists of powdered milk, sugar, and flour in a ratio of 3:4:13.
How many pounds of each ingredient do you need to make 4 lb of baking mix?

Answers

Answer:

Sugar = 0.8 lb

milk = 0.6 lb

Flour = 2.6 lb

Step-by-step explanation:

Firstly, we add the ratios = 3 + 4 + 13 = 20

For milk, we have 3/20 * 4 = 12/20 = 0.6 lb

For sugar l, we have 4/20 * 4 = 16/20 = 0.8 lb

For flour = 13/20 * 4 = 52/20 = 2.6

You will need:

[tex]Milk = 0.6 $ lb\\Sugar = 0.8 $ lb\\Flour = 2.6 $ lb[/tex]

Given:

Milk : Sugar : Flour = 3 : 4 : 13

To find the number of pounds of each ingredient required to produce 4 lb of baking mix, solve as follows:

Amount of each ingredient needed = ratio of each ingredient / total ratio value x 4 lb

Thus:

Total ratio value = [tex]3 + 4 + 13 = 20[/tex]

Amount of milk needed = [tex]\frac{3}{20} \times 4 = 0.6 $ lb[/tex]

Amount of Sugar needed = [tex]\frac{4}{20} \times 4 = 0.8 $ lb[/tex]

Amount of Flour needed = [tex]\frac{13}{20} \times 4 = 2.6 $ lb[/tex]

Therefore, you will need the follow amounts to make 4 lb of baking mix:

[tex]Milk = 0.6 $ lb\\Sugar = 0.8 $ lb\\Flour = 2.6 $ lb[/tex]

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Please help!!! will give brainliest

Answers

Answer:

Angle D

Step-by-step explanation:

If you flip the triangle upside down, Angle D should be in the same location as Angle A. Congruent triangles will have corresponding congruent angles.

Please help me right away and you will get 12 points I need it done today so plz help me

Answers

Answer:

all u have to do is add up the denominator and numerators together because just because u see something as an add problem it's still more stuff to add 6+8=14 7+5=12 add up 14+12=26+blank=what

Step-by-step explanation:

hopefully this helped

a=4, b=2 and c=-3
who wanna tell me the answer lol my Photomath won’t tell me

Answers

Answer:

-23

Step-by-step explanation:

Answer:

-23

Step-by-step explanation:

Just plug in the values of the variables into the expression. You'll get -4(10)/2 - 3. That equals -20 - 3, or -23.

I create art do you like it

Answers

Not bad keep working on your technique

Answer:

YES!!! It really cool, you should create an Instagram account and post you art there!!

Step-by-step explanation:

Knowing that GB is 18 and CD = 21 you should be able to use them to solve this problem.

Answers

9514 1404 393

Answer:

FG = 9BF = 27GD = 7CG = 14

Step-by-step explanation:

Point G is the intersection of medians, the centroid. That point divides each median into parts with a 2:1 ratio. The "2" part is the distance between the centroid and the vertex. The "1" part is the distance between the centroid and the side.

  FG : GB : BF = 1 : 2 : 3 = 9 : 18 : 27 . . . . . where 18 is given

  GD : CG : CD = 1 : 2 : 3 = 7 : 14 : 21 . . . . . where 21 is given

Plot the image of point Q under the translation (x, y) + (x - 3, y + 4).​

Answers

Answer:

( 2, -1 )

Step-by-step explanation:

The image of the assumed point Q(2, 3)) under the translation is Q'(-1, 7).

What is Translation?

Translation is a type of transformation of geometrical figures. After translation, the original figure is shifted from a place to another place without affecting it's size.

Translation of a point (x, y) indicates that the point is moved x units along the X axis and y units along the Y axis,

Here we have to translate the point Q(2, 3).

Point (x, y) is translated as (x - 3, y + 4).

That is the point (x, y) moves 3 units to the left along the X axis and 4 units upwards along the Y axis.

Q(2, 3) after the translation becomes,

Q'(2 - 3, 3 + 4) = Q'(-1, 7)

Hence the point Q(2, 3) under the translation (x - 3, y + 4) is the point Q'(-1, 7).

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A school printed 315 tickets to the spring dance. There are 255 tickets left. Which equation can be used to find how many tickets have been sold?

Answers

You didn't add any options but here's one that would work.

315 - 255 = 60

When there is a problem asking how many are left, taken, sold, given, etc. You are usually dealing with subtraction.

Hope that helps and have a great day!

Answer:

The last choice (x+255=315 )

Step-by-step explanation:

This is because we know the total number of tickets is 315 and they have 255 left. So, x + 255 = 315. Because you subtracted __ from 315 to get 255. You can rewrite that as __ + 255 = 315 or  x + 255 = 315

Can I have help with an algebraic equation?

Answers

Answer:

What is the equation?

Step-by-step explanation:

Answer:

Step-by-step explanation: what is the probelm i can help.

Use the graph and the translation (x,y) (x+1,y+4) to answer parts a and b below

Answers

Answer:

Step-by-step explanation:

Enter the image of each vertex as an ordered pair.

A -> A = (-7,7)

B -> B = (-1,3)

C -> C = (-4,2)

Graph the​ pre-image and image of  ABC. Choose the correct graph below.

Answer is C

The ratio of juniors to seniors on the track team is 6:7. How many juniors are on the track team if there are 21 seniors on the team?


answer: 18

Answers

Answer:

There are 18 juniors on the track team

Answer:

There are a total of 18 juniors on the track team.

Step-by-step explanation:

Apply the following ratio to the quantity by multiplying.

6:7 = 6 to 7 or 6/7

6/7 × 21 = 126/7 = 18

What is the equation of the line that passes through the point (5,1) and has a slope
of 6/5?

Answers

Answer:

y-1 = 6/5(x-5) Point slope form

y-1=6/5x - 6

y-1 +1=6/5x -6+1

y = 6/5x - 5 Slope intercept form

y -6/5x + 5 = 6/5x-5 -6/5x+5

y-6/5x+5=0 General Form

How do you decide in what way to reorder the terms of expression when simplifying it

Answers

The order for simplifying algebraic expression is always the same starts with any parentheses in the problem

We use the PEMDAS to reorder the terms of expression when simplifying it.

What is an expression?

One mathematical expression makes up a term. It might be a single variable (a letter), a single number (positive or negative), or a number of variables multiplied but never added or subtracted. Variables in certain words have a number in front of them. A coefficient is the number used before a phrase.

We use the PEMDAS to reorder the terms of expression when simplifying it.

The abbreviation PEMDAS is used to indicate the sequence of steps to be taken when resolving expressions with multiple operations. P is for "parentheses," E is for "exponents," M is for "multiplication," D is for division, A is for addition, and S is for subtraction.

Therefore, use PEMDAS to simplify any expression.

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What is the perfect square of 4 with an exponent of 2

Answers

Answer:

[tex]\sqrt{4^{2}[/tex] = 4

Step-by-step explanation:

the square root cancles out the exponet because it's just the same thing. One is a negative impact the other is positive.

The length of a rectangle is (5x − 1) cm and the width is (11 − 2x) cm. If the perimeter of the rectangle is 44 centimeters, what is the area of the rectangle?

Answers

Answer:

57 cm²

Step-by-step explanation

l = length

w = width

p = perimeter

(5x - 1) = length

(11 - 2x) = width

44 = perimeter

Formula for the perimeter of a rectangle:

l + l + w + w

2l + 2w = p

Substitute the variables for the length and width with the values given to you by the problem, then solve.

2(5x - 1) + 2(11 - 2x) = 44

(10x - 2) + (22 - 4x) = 44 (Distributive property)

6x + 20 = 44

6x = 24

x = 4

Plug x = 4 back into the length and width.

Length = (5x - 1), (5(4) - 1), (19)

Width =  (11 - 2x), (11 - 2(4)), (3)

Area for a rectangle: Length × Width = Area.

19 × 3 = 57 cm²

This is all in cm so answer with cm²

If the area of a rectangle is 100, then the length is 25 and the width is 4

Answers

Answer:

Yes.

Step-by-step explanation:

since area is length x the width, so in this case it would be 25 x 4 = 100

find the values of a and b​

Answers

Answer:

Im not sure about a but, b= 38

Step-by-step explanation

b: 90 - 52 = 38

*90 because it is a right angle

How do I solve 3 (9-5)² ÷8 ?

Answers

Answer:

3(9-5)^2 ÷8

3(4)^2÷8

3(16)÷8

3(2)=6

Answer:

6

Step-by-step explanation:

9-5=4

=4

3×4^2 ÷ 8

4^2=16

3×16 ÷8

3×16=48

48÷8=6

(PLEASE ANSWER ILL GIVE YOU 20 POINTS) Determine if the relation is a function. If the relation is a function, find the domain and range.Required to answer. Single choice.

Answers

Answers:

The relation is a function

Domain = {-2, -1, 0, 1, 2}

Range = {-2, 0, 2}

=================================================

Explanation:

The blue points shown are

(-2,-2)

(-1,0)

(0,2)

(1,0)

(2,-2)

Note how the x values do not repeat themselves. Visually this graph passes the vertical line test. It is impossible to draw a single straight vertical line through more than one blue point at a time. It tells us that any x input leads to exactly one y output.

The relation is a function

The domain is the set of x coordinates of the points

Domain = {-2, -1, 0, 1, 2}

The range is the set of y coordinates of each point

Range = {-2, 0, 2}

Toss out any duplicate items that may occur in the range.

Answer:

The relation is a function.

The domains are 2, 1, 0, -1, -2.

The ranges are -2, 0, 2, 0, -2

If f (x) = one-ninth x minus 2, what is f>1(x)

Answers

Answer: f-1(x) = 9x + 18.

Step-by-step explanation:

let y = f(x) and rearrange making x the subject, that is

y =  x - 2 ( add 2 to both sides )

y + 2 =  x

Multiply through by 9 to clear the fraction

9y + 18 = x

Change y back into terms of x

(x) = 9x + 18

Answer:

Answer: f-1(x) = 9x + 18.

Step-by-step explanation:

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