Which of the following recursive formulas represents the same arithmetic sequence as the explicit formula an = 5+ (n-1)2?

Which Of The Following Recursive Formulas Represents The Same Arithmetic Sequence As The Explicit Formula

Answers

Answer 1

Answer:

[tex]a_1 = 5[/tex]

[tex]a_n = a_{n-1} + 2[/tex]

Step-by-step explanation:

Given

[tex]a_n = 5 + (n - 1)2[/tex]

Required

The equivalent recursive function

The general explicit function is:

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

So, by comparison

[tex]a_1 = 5[/tex]

[tex]d = 2[/tex]

The recursion of an arithmetic sequence is:

[tex]a_n = a_{n-1} + d[/tex]

Substitute 2 for d

[tex]a_n = a_{n-1} + 2[/tex]

Hence: (a) is correct


Related Questions

Liang bought a basket of apples to make pies for her friends. The basket of apples weighed ppp pounds. Before she had time to make the pies, she ate 3 pounds of apples. There are 17 pounds of apples left to make pies.

Answers

Answer: The equation to describe the situation is  p-3= 17

And, the total weight of the basket of apples was 20 pounds.

Step by step: Now, to write an equation to describe the situation. And to find the total weight of the basket of apples.

So, the basket of apples total weighed = p pounds

Liang ate apples weighed = 3 pounds.

And the apples left for the pies weighed = 17 pounds.

Now, to write an equation describing the situation:

p-3=17 .

Thus, the equation is p-3=17

Now, to get the total weight of the basket of apples:

p-3=17

adding both sides by 3 we get : p=20

Hence, the basket of apples total weighed = 20 pounds.

Therefore, the equation to describe the situation is p-3=17

And, the total weight of the basket of apples was 20 pounds.

THIS SHOULD HELP U

HAVE A GOOD DAY !

Kenya solved the equation below. Negative 6 (x minus 2) + 3 x = negative 3 (x + 3) + 21 What is the solution to Kenya's equation? –4 12 no solution infinitely many solutions

Answers

Answer: No solution

Step-by-step explanation:

-6(x - 2) + 3x = -3(x + 3) + 21

-6x + 12 + 3x = -3x - 9 + 21

Collect like terms

-6x + 3x + 3x = -9 + 21 - 12

-6x + 6x = - 9 + 9

0 = 0

In this scenario, it can be deduced that there is no solution to Kenya's equation.

Answer:

infinitely many solutions

Step-by-step explanation:

i got it right

Professor Goodheart has two exams, exam 1 and exam 2. The exam 1 weights 40% and the exam 2 weights 60% of the final grades. Put the grades on the exam 1 on the horizontal axis and the grade on the exam w on the vertical axis. What kind of preference a student should have for these two grades

Answers

Answer:

Imperfect substitutes

explanation:

The choices above are not perfect substitutes, meaning they can not be perfectly or directly replace the other. Imperfect substitutes are close substitutes but not perfect substitutes. Unlike perfect substitutes, imperfect substitutes satisfies same utility but has different characteristics and therefore not entirely substitutable. For example, while one may want to have the 40 marks too, he'd rather have 60 marks even if the criteria for a 60 mark score was increasingly hard.

Will Mark Brainlest helpppp​

Answers

Answer:

R = [tex]\left[\begin{array}{ccc}-3&-2\\1&-3\\\end{array}\right][/tex]

Step-by-step explanation:

P - Q + R = I ( I is the identity matrix )

[tex]\left[\begin{array}{ccc}2&4\\3&5\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}-2&2\\4&1\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] ( subtract corresponding elements )

[tex]\left[\begin{array}{ccc}2-(-2)&4-2\\3-4&5-1\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

[tex]\left[\begin{array}{ccc}4&2\\-1&4\\\end{array}\right][/tex] + R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex]

R = [tex]\left[\begin{array}{ccc}1&0\\0&1\\\end{array}\right][/tex] - [tex]\left[\begin{array}{ccc}4&2\\-1&4\\\end{array}\right][/tex] = [tex]\left[\begin{array}{ccc}-3&-2\\1&-3\\\end{array}\right][/tex]

the circumference of a circle is 11pi ft. find its diameter, in feet​

Answers

Answer:

The diameter would be 11 feet

Step-by-step explanation:

C = pi * d

we don't know D so we rearrange the equation to solve for D by dividing both sides by pi:

C/pi = d

Now we plug in everything

11pi/pi = d

The pi cancel each other out leaving with 11 feet

Therefore D = 11 feet

1-tanx/1+tanx=1+sin2x

Answers

are you sure about the ques?

Solve simultaneous equations 3x-2y=17 +2x-2y=10

Answers

Answer:

(7;2)

Step-by-step explanation:

[tex]3x - 2y = 17 \\ - 2y = 17 - 3x \\ 2x + 17 - 3x = 10 \\ 2x - 3x = 10 - 17 \\ - x = - 7 \\ x = 7 \\ - 2y = 17 - 21 \\ - 2y = - 4 \\ y = 2[/tex]


Helppp plssss help meeee

Answers

Answer:

C. $1,260

Step-by-step explanation:

80 × 14.5 = 1,160

2,500 × 0.04 = 100

Answer:

C. $1260

Step-by-step explanation:

What is the area of this triangle?

Answers

I can't type it I have to solve on a paper for you

Please help me get the answers

Answers

Answer:

1. (4)

2. (2)

Step-by-step explanation:

what is y=2x*2-6x-8 as a graph ​

Answers

Answer:

[tex] \bf \: y = 2 {x}^{2} - 6x - 8[/tex]

It is equation of a parabolla.

It is to be noted that the graph of y = 2x * 2-6x-8 which when simplified is  y = -12x² - 12x. is attached accordingly.

What are the qualities of the graph of y = -12x² - 12x?

The graph of y = -12x² - 12x is a downward-opening parabola.

It has a concave shape and its vertex is the highest point on the graph. The axis of symmetry is a vertical line passing through the vertex.

The graph may intersect or be tangent to the x-axis at two points, one point, or no points, depending on the discriminant.

Learn more about Graph at:

https://brainly.com/question/19040584

#SPJ6

x(x - 2) = 4 please help

Answers

Answer:

[tex]x = 1 + \sqrt{5} x = 1 - \sqrt{5} [/tex]

plss help me with this :(​

Answers

Answer:

(k) cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)

From trigonometric identities, we have;

1 + cot²θ = cosec²θ

On the Left Hand Side of the equation, we get;

cos(θ)·√(1 + cot²θ) = cos(θ) × cosec(θ) = cot(θ)

On the Right Hand Side of the equation, we have;

√(cosec²(θ) - 1) = √(1 + cot²(θ) - 1) = √(cot²(θ)) = cot(θ)

∴ √(cosec²θ - 1) = cot(θ)

By transitive property of equality, therefore;

cos(θ)·√(1 + cot²θ) = √(cosec²θ - 1)

(l) sin⁶A + cos⁶A = 1 - 3·sin²A·cos²A

sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³

(sin²A)³ + (cos²A)³ = ((sin²A) + (cos²A))³ - 3·((sin²A)·(cos²A))·((sin²A) + (cos²A))

∴ (sin²A)³ + (cos²A)³ = (1)³ - 3·((sin²A)·(cos²A))·(1) = 1 - 3·((sin²A)·(cos²A))

sin⁶A + cos⁶A = (sin²A)³ + (cos²A)³ = 1 - 3·((sin²A)·(cos²A))

sin⁶A + cos⁶A = 1 - 3·((sin²A)·(cos²A))

(m) (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1

(sinA - cosecA)²  = sin²A - 2×sinA×cosecA + cosec²A = sin²A - 2 + cosec²A

(cosA - secA)² = cos²A - 2×cosA×secA + sec²A = cos²A - 2 + sec²A

∴ (sinA - cosecA)² + (cosA - secA)² = sin²A - 2 + cosec²A + cos²A - 2 + sec²A

Where;

sin²A - 2 + cosec²A + cos²A - 2 + sec²A = sin²A + cos²A  - 2  - 2 + cosec²A + sec²A

sin²A + cos²A  - 2  - 2 + cosec²A + sec²A = 1 - 4 + cosec²A + sec²A

1 - 4 + cosec²A + sec²A = cosec²A + sec²A - 3

Where;

cosec²A = cot²A + 1

sec²A = tan²A + 1

∴ cosec²A + sec²A - 3 = cot²A + 1 + tan²A + 1 - 3 = cot²A + tan²A - 1 = The Right Hand Side of the equation

∴ (sinA - cosecA)² + (cosA - secA)² = cot²A + tan²A - 1

(n) [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA

Squaring the Right Hand Side of the equation, we get;

(sinA - cosA)² = sin²A -2·sinA·cosA + cos²A = sin²A + cos²A -2·sinA·cosA

sin²A + cos²A -2·sinA·cosA = 1 - 2·sinA·cosA

∴ (sinA - cosA)² =  1 - 2·sinA·cosA

Taking the square root of both sides gives;

√((sinA - cosA)²) = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]

∴ sinA - cosA = [tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex]

By symmetric property of equality, we have;

[tex]\sqrt{1 - 2\cdot siaA\cdot cosA}[/tex] = sinA - cosA

Step-by-step explanation:

A company's stock price flucated over a period of four days. The table shows the change in stock price per day. The net change in the company's stock price over the four days

Answers

Answer:

The net change is -.30

Step-by-step explanation:

increase means add

decrease means subtract

+3.50

-3.70

+3.30

-3.40

-------------

-.30

The net change is -.30

Instructions: Given the following coordinates complete the glide reflection
transformation.
A(-9,-2)
B(-9,-5)
C(-5,-4)
Transformation: Reflection over the y-axis and a translation of shifting up 5 units

Answers

Answer:

A(9,3)

B(9,0)

C(5,1)

Step-by-step explanation:

How many solutions does this equation have x^4 - 6x^2 -7 = 0

Answers

Answer:

2 solutions

Step-by-step explanation:

x^4-6x^2-7=0

Replace x^2 by y

(x^2)^2-6x^2-7=0

y^2-6y-7=0

D=b^2-4ac= (-6)^2-4*1*(-7)= 36+28=64

sqrtD=8

y1=(-b-sqrtD)/2a=-2/2=-1

y2= (-b+sqrtD)/2a=14/2=7

x^2=-1(n0 roots)    x^2=7 x=sqrt7 or x=-sqrt7

2 roots

Question 8 If f (2) = (1 + 3) and g (2) VO+ 7, find g (f (x)). 9(f()) = 1 + 10 O g(f ()) = VI + 3 +7 Og(f (x)) = v= + 10 Og(f (2)) = 2? + 10​

Answers

Answer:

x+10

Step-by-step explanation:

f(x) = (x+3)^2 and g(x) = sqrt(x)+7

g(f(x)) =

Replace f(x) in for x in the function g(x)

        = sqrt((x+3)^2)+7

        = x+3 +7

         = x+10

please help with me

Answers

360-53-44-46= 217 (reflex angle)

Answer:

217

Step-by-step explanation:

53 + 44 + 46 = 143

360 - 143 = 217

Please help me with this I need it

Answers

9514 1404 393

Answer:

  2/3

Step-by-step explanation:

Let x represent the fraction of Cheryl's income she spent in September. Then 1-x is the fraction she saved.

In October, her spending increased by 0.2x, and her savings decreased by 0.4(1 -x). Since Cheryl spends or saves all of her income, these two change amounts must be equal:

  0.2x = 0.4(1 -x)

  x = 2(1 -x) . . . . . . multiply by 5 to clear fractions

  x = 2 -2x . . . . . . eliminate parentheses

  3x = 2 . . . . . . . . add 2x

  x = 2/3 . . . . . . divide by 3

Cheryl spent 2/3 of her income in September.

what should I do?
in the picture

Answers

The expression has y and x variables in denumerator and numerator, these variables will form the results as y^1/2 / x^3/2.

This expression is given in choice A.

The correct expression will place the y in denomerator with change in power sign in the numerator and x value will become in denomerator form the expression under root power 3 over 2.

Learn more at https://brainly.com/question/24378446

In a city of 26000 populations, 5000 read English newspaper, 12000 read Nepali newspaper and 1000 read both. What percentage read neither English and Nepali newspaper? ( from set theory )

Answers

Answer:

38.46%

Step-by-step explanation:

total readers=16000

population=26000

no of non-readers=total population-total readers

=26000-16000

=10000

percentage of non-readers=non-readers×100%

population

=10000×100%

26000

percentage of non-readers is 38.46%

If a and b are parallel and c and d are parallel, which pair of angles are congruent?

A. 1 and 16
B. 5 and 8
C. 9 and 11
D. 12 and 13

Answers

was there any pic added to this equation?

Write equivalent expressions.

1. 5(a+a+a)= ________________________________________________________________________

2.6(3x-4)=____________________________________________________________ _______​

Answers

Answer:

15a

18x -24

Step-by-step explanation:

5(a+a+a)

Combine terms in the parentheses

5(3a)

Multiply

15a

6(3x-4)

Distribute

18x -24

Will give us many points as possible thank you very much

Answers

Answer:

27 1/2 cm^2

Step-by-step explanation:

The area of a parallelogram is

A = bh

A = 5 * 5 1/2

Change to an improper fraction

A = 5 * (2*5+1)/2

A = 5*11/2

A = 55/2

Change back to a mixed number

A = 27 1/2

Click an item in the list or group of pictures at the bottom of the problem and, holding the button down, drag it into the correct position in the answer box. Release your mouse button when the item is place. If you change your mind, drag the item to the trashcan. Click the trashcan to clear all your answers.

A(1, 1), B(-3, 0), C(-4, -1), D(3, -2)

Answers

Answer:

is this geomtey

Step-by-step explanation:

Make sure to put what kind of maths (geometry algebra ect.) this is so others can meet your needs better. Also might want to put what unit or type of problem this is as well.

Si confused as to how to solve this

Answers

Answer:

x^2, 10-x , 1.5x -5  

Step-by-step explanation:

CAN SOMBOBY HELP ME find the surface area of each figure. Round it to the nearest tenth if necessary.​

Answers

Answer:

365.65

Step-by-step explanation:

you can find the formula online

Right circular cone.
Solve for surface area.
A - 389.85.
Radius.
h.
Height.
13.4.
Using the formulas.
A= arl+ar².
Vithi.
Solving for A.
A= ar (r+.
\/h²+r ).
= T·6·(6+/ 13.4+6' )~ 389.84579.

hat is the measure of x?
X = [?]
D
126

Answers

Answer:

since those are angles on a straight line.

we work out as follows

x+126°=180°x+126°-126°=180°-126°x=54°

∠DBA and ∠DBC are making linear pair.

Linear pair of angles are formed when two lines intersect each other at a single point.

The sum of angles of a linear pair is always equal to 180°

[tex]\rm \large\longrightarrow \: \: x \: + \: 126 \degree \: = \: 180 \degree[/tex]

[tex]\rm \large\longrightarrow \: \: x \: = \: 180 \degree \: - \: 126 \degree [/tex]

[tex]\rm \large\longrightarrow \: \: x \: = \: 54 \degree[/tex]

Factor the polynomial x^2+9x+8 using the pattern x^2+(a+b)x+ab=(x+a)(x+b)

Answers

Answer: final answer is (x+1) (x+8)

We need two numbers that...

Add together to get 9

Multiply together to get 8

Try 1 and 8:

1+8 = 9

1*8 = 8

therefor the answer is  (x+1) (x+8)

The volume of a prism with side lengths measured in millimeters is 20. How could this measurement be written? Check all that apply.

20 millimeters
20 mm3
20 mm2
20 square millimeters
20 cubic millimeters

Answers

Answer:

20 mm^3, 20 cubic millimeters

Step-by-step explanation:

The volume of a prism is length times width times height.

Length, width, and height can have units of mm.

mm * mm * mm = mm^3

The units of a volume must be cubic units.

Answer: 20 mm^3, 20 cubic millimeters

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