what is the explicit formula for this sequence

What Is The Explicit Formula For This Sequence

Answers

Answer 1

Answer:

A

Step-by-step explanation:

Start with the 3.

You know that there is a difference of 4 between (say) 2 and 5. The 3 is a sign that the sequence is increasing.  The members of the sequence are going up.

n - 1 means that the nth terms is calculated as an and uses the number of terms to be n-1. That means that the first term is a1 which is the starting point of the sequence.

The answer is an = a1 + (n-1)*d

d = 3

a1 = - 7

So let's try the formula out.

a4 = -7 + (4 - 1)*3

a4 = -7 + 3 * 3

a4 = -7 + 9

a4 = 2

Is 2 the 4th term in the series? Yes it is!


Related Questions

Identify the construction that the figure represents

Answers

Answer:

Not sure if this will help but that looks like a bisection of angles BAC and TSR.

This is the recursive formula for a geometric sequence:
f(1)=8,000
f(n)=1/2(n − 1), for n > 2
What is the fifth term in the sequence?

Answers

Answer:

Step-by-step explanation:

f(1) = 8000

f(2) = 1/2(n - 1)

f(2) = 1/2(2 - 1)

f(2) = 1/2    Note: this really does not make sense. I think what you mean is 1/2*f(n-1). If this is true, leave a note within the next hour.

Answer:

f(5) = 500

Step-by-step explanation:

Using the recursive rule and f(1) = 8000 , then

f(2) = [tex]\frac{1}{2}[/tex] f(1) = [tex]\frac{1}{2}[/tex] × 8000 = 4000

f(3) = [tex]\frac{1}{2}[/tex] f(2) = [tex]\frac{1}{2}[/tex] × 4000 = 2000

f(4) = [tex]\frac{1}{2}[/tex] f(3) = [tex]\frac{1}{2}[/tex] × 2000 = 1000

f(5) = [tex]\frac{1}{2}[/tex] f(4) = [tex]\frac{1}{2}[/tex] × 1000 = 500

An equilateral triangle has a perimeter of 15x3 + 33x5 feet. What is the length of each side?
x3 feet
5 + 11x2 feet
5x2 + 11 feet
5x3 + 11x5 feet

Answers

Answer:

the answer is 5×3+11×5 feet

Answer:

4th option

Step-by-step explanation:

An equilateral triangle has 3 congruent sides

Divide the perimeter by 3 for length of side

[tex]\frac{15x^3+33x^5}{3}[/tex]

= [tex]\frac{15x^3}{3}[/tex] + [tex]\frac{33x^5}{3}[/tex]

= 5x³ + 11[tex]x^{5}[/tex] ← length of 1 side

A payday loan store charges $25 for a one-month loan of $600. What annual interest rate is this equivalent to?

Answers

Answer:

50%

Step-by-step explanation:

1. determine the monthly interest rate

monthly interest rate = interest / loan amount

monthly interest = 25 / 600 = 4.17%

2, multiply the monthly interest rate by 12 to determine the annual interest rate

Annual interest = 4.17 x 12 = 0.5 = 50%

Which of the following polynomial equations has 1, 4, -5 as three of its roots?

x 2+4x-5=0
x 4+2x 3-5x+10=0
x 3-21x+20=0*

Answers

Answer: x³-21x+20=0

Step-by-step explanation:

To find which polynomial has 1, 4, -5 as the roots, all we have to do is equal each root to 0 and multiply all factors together.

1 is (x-1)=0

4 is (x-4)=0

-5 is (x+5)=0

Now, we just multiply them together.

(x-1)(x-4)(x+5)=0                       [FOIL]

(x²-4x-x+4)(x+5)=0                    [combine like terms]

(x²-5x+4)(x+5)=0                      [FOIL]

x³+5x²-5x²-25x+4x+20=0       [combine like terms]

x³-21x+20=0

Now we know x³-21x+20=0 is the polynomial with those roots.

Jo bought a used car for $6000 and paid a 15% deposit. How much did he still have to pay?

Answers

Answer:

900 is the correct awnser

State the slope of the line shown below (help ASAP)
Is it a, b, c or d?

Answers

Answer:

D

Step-by-step explanation:

(the above graph depicts a horizontal line that intersects the y axis at -2)

(so, y = -2)

Answer:

0

Step-by-step explanation:

Horizontal line x axis is 0 while the vertical y axis is undefined.

what is value of y if 2x+3y=4​

Answers

Answer:

y=(4-2x)/3

Step-by-step explanation:

3y= 4-2x

y= (4-2x)/3

hlp pleassssssssssssssssssssss

Answers

Answer:

Volume of a cube is s×s×s

hence 7 cube=343

343 is the answer. Hope this helps you. Good luck^_^

Which statement is true about figures ABCD and A'B'C'D'?
у
5
4
c
3/
D'
B
2
1 2 3 4 5
1
A
-5 -4 -3 -2 -1 0
AS - 1
-2
D
B
с
-41
-31

Answers

When figures are translated, rotated or reflected, the resulting figures are congruent to the original figure because the transformations are rigid. However, when a figure is dilated, the resulting figure is not congruent to the original figure.

ABCD and A'B'C'D are congruent because A'B'C'D is the result of rotating ABCD 180 degrees about the origin.

I've included the missing graph as an attachment.

Using points A and A' as our references.

We have:

[tex]A = (-1,1)[/tex]

[tex]A' = (1,-1)[/tex]

The rule of rotation 180 degrees about the origin is:

[tex](x,y) \to (-x,-y)[/tex]

So, we have:

[tex](-1,1) \to (-(-1),-1)[/tex]

[tex](-1,1) \to (1,-1)[/tex]

The above rule is applicable to other points in ABCD and A'B'C'D'

Since the rule of transformation is rotation (a rigid transformation), then ABCD and A'B'C'D are congruent.

Read more at:

https://brainly.com/question/9475847

which number best completes the pattern ?
17,12,7
3,7,11
21,16(?)

a. 12 b. 11 c. 8 d. 3​

Answers

Answer:

11

Step-by-step explanation:

the common difference in the last sequence is 5 which can be gotten by subtracting the first term minus the second term.. therefore to find the next term you subtract 5 from the previous term,and 16-5 is 11.

I hope this helps

Answer:

b

Step-by-step explanation:

The first series has a patten which is an=a(n-1)-5. The second series follow the pattern which is an=a(n-1)+4. The third series follow the pattern an=a(n-1)+5. So 16-5=11.

Which of the following could be the value of xy if y = 7and x>7?

Answers

Answer:

Any number greater than 49.

Step-by-step explanation:

Since 7>0 then multiplying both sides of x>7 by 7 will not effect the direction of the inequality.

If x>7, then 7x>7(7) or 7x>49 after simplifying.

Substituting y for 7 since y=7 gives yx>49.

By commutative property of multiplication we have xy>49.

So any number greater than 49.

C. Examine the hourglasses (A), (B), and (C) and
find the best answer.
6
(A)
(B)
.(C)
6
a) (B) shows the most time passed.
b) (A) shows the most time passed.
c) (C) shows the most time passed.
d) (A), (B), and (C) show the same time passed.
6

Answers

Answer:add a screenshot

Step-by-step explanation:

I can't see the our glasses

[tex](a+b)^{2}[/tex]

Answers

Answer:

[tex] ({a + b})^{2} [/tex]

[tex](a + b)(a + b)[/tex]

[tex] {a}^{2} + 2ab + {b}^{2} [/tex]

hope this help you

HELP ME ASAP !!!!! ITS DUE TODAY

Answers

Answer a:

Figure 4 = 5 blocks up, 5 blocks right

Figure 5 = 6 blocks up, 5 blocks right

Answer b: Grows 2 blocks each time, 1 blocks at the top and 1 blocks on the right.

Answer c: Since you add 2 blocks each time, you do the opposite so you subtract 2 blocks. The answer will be 1 block.

Step-by-step explanation:

Which equation can be used to find the unknown length, b, in this triangle?


Answers

Answer: Choice A

4^2 + b^2 = 5^2

This is due to the pythagorean theorem.

what is the value for f(x)4^2x -100 when x=2 ?

(the ^2x is a exponent)

Answers

Answer:

156

Step-by-step explanation:

f(x)= 4^(2x) -100

Let x =2

f(2)= 4^(2*2) -100

   = 4^4 - 100

   = 256 -100

   = 156

how do i solve this?

Answers

Answer:

f(3) = 2

General Formulas and Concepts:

Pre-Algebra

Order of Operations: BPEMDAS

Brackets Parenthesis Exponents Multiplication Division Addition Subtraction Left to Right

Algebra I

Functions

Function Notation

Step-by-step explanation:

Step 1: Define

Identify

f(x) = 2x - 4

Step 2: Evaluate

Substitute in x [Function f(x)]:                                                                           f(3) = 2(3) - 4Multiply:                                                                                                             f(3) = 6 - 4Subtract:                                                                                                            f(3) = 2

What is the standard form for the quadratic function? g(x)=(x−6)2−5

Answers

Answer:

x^2-12x+31

Step-by-step explanation:

Standard form of the quadratic equation (x-6)^2-5 is x^2-12x+36-5=x^2-12x+31

what is the GCF of 18 and 36

Answers

Answer: 18

Step-by-step explanation: Factor of 18 are: 1, 2, 3, 6, 9, 18

Factor of 36 are : 1, 2, 3, 4, 6, 9, 12, 18, 36

Hope that helps

Answer:

18

Step-by-step explanation:

listing the factors

factors of 18 are 1, 2, 3, 6, 9, 18

factors of 36 are 1, 2, 3, 4, 6, 9, 12, 18, 36

The common factors are 1, 2, 3, 6, 9, 18

with GCF being 18

Please solve the problem ​

Answers

Treat the matrices on the right side of each equation like you would a constant.

Let 2X + Y = A and 3X - 4Y = B.

Then you can eliminate Y by taking the sum

4A + B = 4 (2X + Y) + (3X - 4Y) = 11X

==>   X = (4A + B)/11

Similarly, you can eliminate X by using

-3A + 2B = -3 (2X + Y) + 2 (3X - 4Y) = -11Y

==>   Y = (3A - 2B)/11

It follows that

[tex]X=\dfrac4{11}\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\dfrac1{11}\begin{bmatrix}7&-10\\-7&11\end{bmatrix} \\\\ X=\dfrac1{11}\left(4\begin{bmatrix}12&-3\\10&22\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\left(\begin{bmatrix}48&-12\\40&88\end{bmatrix}+\begin{bmatrix}7&-10\\-7&11\end{bmatrix}\right) \\\\ X=\dfrac1{11}\begin{bmatrix}55&-22\\33&99\end{bmatrix} \\\\ X=\begin{bmatrix}5&-2\\3&9\end{bmatrix}[/tex]

Similarly, you would find

[tex]Y=\begin{bmatrix}2&1\\4&4\end{bmatrix}[/tex]

You can solve the second system in the same fashion. You would end up with

[tex]P=\begin{bmatrix}2&-3\\0&1\end{bmatrix} \text{ and } Q=\begin{bmatrix}1&2\\3&-1\end{bmatrix}[/tex]

Step-by-step explanation:

hence it has been done . check the file .

hope this helped you

any problem then comment it .

Help? Please! I need hElppz

Answers

Answer:

-29

Step-by-step explanation:

- 22 - □ = 7

=> - 22 - 7 = □

=> - 29 = □

=> □ = - 29 (Ans)

1.Waheeda mixes water with some lemon juice to make lemonade. Write an equation to represent how much lemon juice is needed when Waheeda uses 18 ounces of water.

2. Identify the independent and dependent variables in the situation.
Independent variable: Dependent variable: b) Write an equation representing the amount Waheeda earns in relation to the number of glasses of lemonade she sells.
Equation: c) In which Quadrant of a graph would her data appear? Explain.

Answers

1. The equation is 18 = 3 × x

2. a) The independent variable is the of ounces of lemon juice in the lemonade

b) A = a × b

c) First quadrant

The procedure to find the above answers are presented here as follows;

1. The following is the table of values of the data

[tex]\begin{array}{ccc} Lemon \ juice \ ounces \ (x)& & Water \ in \ ounces \ (y)\\2&&6\\3&&9\\4&&12\\5&&15\end{array}[/tex]

The given data in the table shows that the Lemon juice ounces, x, and the Water in ounces, y, have a direct proportionality relationship which is given as follows;

y ∝ x

∴ y = k × x

Where;

k = The constant of proportionality

k = y/x

Therefore;

k = 6/2 = 9/3 = 12/4 = 15/5 = 3

k = 3

y = k × x

∴ y = 3 × x

Therefore;

The equation to represent how much lemon juice, x, is needed when Waheeda uses y = 18 ounces of water  is given by placing y = 18 in y = 3 × x as to get;

18 = 3 × x

∴ x = 18/3 = 6; 6 ounces of lemon juice is needed with 18 ounces of water

2. The independent variable is the input or causing variable that determines the output variable

Therefore, the independent variable is the number of ounces of lemon juice required to be mixed with a given number of ounce of water to make lemonade

b) Let a represent the selling price for a glass of lemonade, let b represent the number of glasses of lemonade she sells, and let A represent the amount she earns, we have;

A = a × b

c) The given x and y values in the data are both positive values, which indicate that the data would appear in the first quadrant

Learn more about dependent and independent variable here;

https://brainly.com/question/18456313

Square inscribed in a circle with radius 16.

I’ll mark u as a brainliest!!

Answers

Answer:

if your trying to find the area of the square it's 1024 if your trying to find the circumference of the circle it's 32π ( also known as 32 x pi)

The square of y varies directly as the cube of x.When x=4 y=2.Which equation can be used to find other combinations of x and y

Answers

Answer:

y² = (1/16)x³

Step-by-step explanation:

Given that :

y² varies directly as the cube of x

y² α x³

y² = kx³ - - - (1)

Where, k = constant of f proportionality

We can obtain the value of k ; when x= 4 and y = 2

2² = k4³

4 = 64k

k = 4/64

k = 1/16

Putting k = 1/16 in (1)

y² = (1/16)x³

Why 1975 can't be the sum of two squares. Or prove that the equality x ^ 2 + y ^ 2 = 1975 has no solutions in integers

Answers

Answer:

Step-by-step explanation:

If a number can be expressed by sum of two square, only if the number can be represented by 4k + 1 form

1975 = 4*493 + 3

So, 1975 can't be a sum of two squares

((3.55)^2+(4.12)^2+(4.41)^2)/2(3.55)*(4.12)

Answers

Answer:

((3.55)^2+(4.12)^2+(4.41)^2)/2(3.55)*(4.12)

=358.519825

Step-by-step explanation:

I just used this website called mathpapa.com, extremely useful for algebra calculations. Here's the link if you need it

https://www.mathpapa.com/algebra-calculator.html

John and Pablo caught fish that have the lengths, in centimeters, listed below. 45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44 Which box-and-whisker plot correctly represents the data?

Answers

The options for the box and whisker plots aren't given ; however using technology, a box and whisker plot could be generated from the data.

Answer:

Step-by-step explanation:

Given :

45, 44, 47, 49, 45, 47, 42, 39, 45, 42, 44

Using technology, the box and whisker plot generated for the data is attached below.

The 5 - number summary is also given below :

Minimum: 39

Median: 45

First quartile: 42

Third quartile: 47

Interquartile Range: 5

Maximum: 49

Outliers: none

Answer:

Step-by-step explanation:

If A = {a,b} and B = {1, 2, 3} then, find A×B and B×A and show them by a mapping diagram.

Answers

A × B = {a, b} × {1, 2, 3} = {{a, 1}, {a, 2}, {a, 3}, {b, 1}, {b, 2}, {b, 3}}

Jon and Kristen are both increasing the number of minutes they jog each day, as shown in the tables.

Jon
Day Minutes
0 15
1 17
2 19
3 21
Kristen
Day Minutes
0 22
1 23
2 24
3 25

Which system of linear equations could be used to determine which day they will jog for the same number of minutes, where d represents the day and m represents the number of minutes?

Answers

Answer:

A system of linear equations that could be used to determine which day they will jog the same number of minutes is presented as follows;

m = 2·d + 15

m = d + 22

Step-by-step explanation:

The table of values for the number of minutes Jon and Kristen jog each day is presented as follows;

Jon

[tex]\begin{array}{ccc}Day&&Minutes\\0&&15\\1&&17\\2&&19\\3&&21\end{array}[/tex]

Kristen

[tex]\begin{array}{ccc}Day&&Minutes\\0&&22\\1&&23\\2&&24\\3&&25\end{array}[/tex]

The slope of the data representing Jon's data, m = (21 - 15)/(3 - 0) = 2

Therefore, the equation representing Jon's data is given as follows;

m - 15 = 2·d

m = 2·d + 15

The slope of the data representing Kristen's data, m = (25 - 22)/(3 - 0) = 1

Therefore, the equation representing Kristen's data is given as follows;

m - 22 = d

∴ m = d + 22

The system of linear equations that could be used to determine which day they will jog the same number of minutes is therefore;

m = 2·d + 15

m = d + 22

The answer is in the picture below!

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