Mathematics Middle School

10. An arithmetic sequence has this recursive formula. What is the explicit formula?​

10. An Arithmetic Sequence Has This Recursive Formula. What Is The Explicit Formula?

Answers

Answer 1

Answer:

[tex]a_{n}=45-3n[/tex]

Step-by-step explanation:

Method 1:

Arithmetic sequence is in the form

[tex]a_{n} =a_{1} +(n-1)d\\[/tex]

d is the common difference, can be found by:

[tex]d=a_{n}-a_{n-1}=-3[/tex]

Subtituting the [tex]a_{1}[/tex] and [tex]d[/tex]

You get:

[tex]a_{n}=42+(-3)(n-1)=45-3n[/tex]

Method 2 (Mathematical induction):

Assume it is in form [tex]a_{n}=45-3n[/tex]

Base step: [tex]a_{1} =45-3(1)=42[/tex]

Inducive hypophesis: [tex]a_{n}=45-3n[/tex]

GIven: [tex]a_{n+1} =a_{n}-3[/tex]

[tex]a_{n+1}=45-3n-3=45-3(n+1)[/tex]

Proved by mathematical induction

[tex]a_{n}=45-3n[/tex]

Related Questions

EXPERT HELP I'LL GIVE BRAINLIEST: C or D

Answers

Answer:

Step-by-step explanation:

A=(3.14d^2)/4

A=0.785d^2

A=0.785(10^2)

A=78.5 yd^2

Can yall check my work? Please?
The Question is: A line passes through the points (9, 30) and (18, 30). Which statement is true about the line?
It has a slope of zero because the change in the y-values is 0.
It has no slope because the change in the y-values is 0.
It has a slope of zero because the change in the x-values is 0.
It has no slope because the change in the x-values is 0.

Answers

I’m 99% sure you got it right! Good job!

A grandfather clock was originally priced at $350 but went on sale for 80% off. If Elizabeth bought the grandfather clock and paid 10% sales tax, how much did she pay in total?

Answers

Answer:

105

Step-by-step explanation:

Answer:

$77

Step-by-step explanation:

80% of 350 is 280

it is $280 off so 350-280=70

then the tax, 10% of 70 which is 7

the answer is $77 because 70+7=77

A. 63°

B. 95°

C. 117°

D. 148°

Answers

Answer:

A.63

Step-by-step explanation:

add 85+32

= 117

Total for a trianlge is 180,

Subtract 180 from 117.

180-117 = 63.

answer is B. 95

explanation: it doesn’t have a right angle sign in the corner so it can’t be 90 but it isn’t small enough to be 63

Please give a full explanation and answer on this

Answers

I think it’s Idek I’m dum

Kevin is taking a taxi from the airport to his home. There is a $6 fee for riding in the taxi. In
addition, Kevin must also pay $1 per mile.
Write an equation where m is the number of miles and t is the total cost in dollars of the
taxi ride.

Answers

6+1m= t. That’s the equation for the problem.
1m+6=t

Explanation: 6 is the base number which does not add up as you go on, and the 1m is the miles and every mile he goes, 1 more gets added up and how ever many miles he goes plus 6 is your answer

Simplify the expressions by combining like terms

-4f - 9 - f + 15

Answers

Answer:

-5f    +6

Step-by-step explanation:

-4f - 9 - f + 15

Combine like terms

-4f -f    -9 +15

-5f    +6

Answer:

-5f+6

Step-by-step explanation:

as we add like terms -4f+(-f)=-5f

-9+15=6

hey y’all i just need help with the shading part please help! if you can do this on a piece of paper or show how do it, i’ll give you a brainlest and bonus points thank you.

Answers

You might have to ask the question again, i’m jot sure what exactly the question requires

10 + 20 + 40 + 30 +60 + 70 + 50 + 90 + 80 + 20 =

Answers

Answer:

470

Step-by-step explanation: ...

7x + 9 = 58 i need all the steps

Answers

Answer:

Step-by-step explanation:

7x + 9 = 58

     -9    -9      Subtract 9 from both sides

7x = 49

/7     /7           Divide both sides by 7

x = 7 (this is an apporximation)

Answer:

7

Step-by-step explanation:

1st you need to subtract 9 from both sides like this: 7x+9-9=58-9. and you'll get 7x=49. Then, divide by 7 on both sides like this: 7x/7=49/7. and you'll get x=7.

One batch of cookies requires two eggs and two and a half cups of flour. How many cups of flour are needed to make three and a half batches of cookies? Write and solve a proportion.

Answers

Answer:

multiply 2 1/2 and 3 1/2

Step-by-step explanation: :)

Answer:

im hungry now.

Step-by-step explanation:

help me with this please please pleasee

Answers

Answer:

37.79924

Step-by-step explanation:

37.79924 that will be your answerw

HELP!!!
write the following in algebraic expressions:

Answers

Step-by-step explanation:

Here is the answer for the unkown n(k+m)

Answer:

n*(k+m)

Step-by-step explanation:

Please help my with this question!!! I’ll give brainlist for the correct answer

Answers

Answer:

I think its C

Step-by-step explanation:

Answer:

The answer is c

Step-by-step explanation:

Joe wants to paint a diagonal line across a sign over the door of his office. The sign measures 8 ft. by 6 ft. How long will the diagonal line be?

Answers

the line would be 48 feet long because 6x8 = 48

Answer:

10 ft.

Step-by-step explanation:

By using the pytahgorean theorem a² + b² = c² we can determine the answer of 10 ft. If you do not know already the length and width are the a and the b so a=6 and b=8. by squaring both of these we get a=36 and b=64 (squaring is just the number times itself so 3² would be 3x3) by adding both of these squared values we get 64+36=100 which means that c²=100 so to get our final answer we just take the square root of c² which is the opposite of squaring it. So √100=10 and that is our final answer

Maria rolled a number cube, numbered from 1 through 6, 100 times and recorded the results in this table.
Based on the table, what is the experimental probability of rolling a 2?

a. 1/50
b. 20/100
c. 2/100
d. 20/50

Answers

Answer:

b

Step-by-step explanation:

Answer:

B

Step-by-step explanation:

Do 20 divided 100 to find probability

Triangle ABC and it's transformation Triangle A'B'C are shown describe the transformation.​

Answers

They both are congruent

Plsssssss help meeeeeee

Answers

1.

total surface area Stot = 20.4924225 cm2

lateral surface area Slat = 16.4924225 cm2

bottom surface area Sbot = 4 cm2

2.

total surface area Stot = 46.1079506 ft2

lateral surface area Slat = 37.1079506 ft2

bottom surface area Sbot = 9 ft2

3.

total surface area Stot = 95.0467761 ft2

lateral surface area Slat = 68.0067761 ft2

bottom surface area Sbot = 27.04 ft2

What the first dude said

i need help asap plsss

Answers

Radius = 5 cm

Height = 8 cm

Volume = πr²h

Volume = π(5 cm)² × 8 cm

Volume = π × 25 cm² × 8 cm

Volume = 200π cm³

The answer is C 200 hope that helps

how has your last two minutes been?

Answers

Getting A’s and trying to get points.

Please answer you will get 10 points.

Answers

Answer:

your answer will be 126

Step-by-step explanation:

8x+78=2x+114

8x-2x=114-78

6x=36

x=36/6=6

<B=2(6)+114

= 126

the answer will be 126 umm

help me with this problem

what is

0.96÷10 with the power of 4

Answers

Answer:

0.00008493465

Step-by-step explanation:

This is your answer.

Answer:

10 to the power of 4 equals to 10,000

so it would be 0.96 ÷ 10,000

which would be

0.000096

take what you will have a nice day <:

aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa

Answers

Bbb bbbbbbbbbbbbbbbbb

whats with these random people always answering with "cutlnk.ml/0tj3C" pls ‍♂️

Answers

i dunno why i dont click the links since they are kinda sus and also why doesn't brainly just ban the cutlink

can some one help me asap like pls hurry. and pls some one answer all

Answers

Answer:

10.) J.

11.) D.

12.) G.

13.) B.

14.) i don't know  what this one is sorry

15.) i don't know

16.) H.

sorry if there not right

Step-by-step explanation:

Four triangles are shown. Based on these triangles, which statement is true?

Answers

Answer:

First one

Step-by-step explanation:

100+30=130 That is the rule for finding w

And z=50

Answer: the first one

Step-by-step explanation:

The scale factor from rectangle Y to rectangle Z is 2. Which statement is true?

A) The area of rectangle Z is twice the area of rectangle Y.

B) The area of rectangle Z is half the area of rectangle Y.

C) The sides of rectangle Z are twice as long as the sides of rectangle Y.

D) The angles of rectangle Z are twice as big as the angles of rectangle Y.

Answers

Answer:

Answer is C not A

y=3x+14
2x-3y=-14
Substitution method

Answers

Answer:

x = -8

Step-by-step explanation:

y = 3x + 14

2x - 3y = -14

So, what is the substitution? Y of course, this is because y is equal to 3x + 14.

2x - 3 (3x + 14) = -14

Multiply 3 with the numbers in the parentheses.

2x - 9x + 42 = -14

So you maybe be wondering why it is a negative 7 instead of subtracting 9 with 2. Using PEMDAS, we always read from left to right. So it is basically 2 -9 and you get -7.

-7x + 42 = -14

Then subtract 42 from both sides.

-7x + 42 - 42 = -14 - 42

Simplify

-7x = -56

Divide 7 by both sides.

-7x / 7 = -56 / 7

x = -8

And you might ask, why we get x instead afterwards. This is because both -7 and 7 cancel each other out leaving us with x.

X=-8






I know it’s that so it’s does not need a explanation

Juan works for an agricultural company and is studying the growth of two different types of corn. The table above shows the growth of each type of corn in inches for each month. Compare the centers for both types of corn.

Answers

Answer:

bvghvghvgv

Step-by-step explanation:

bhjbbjuhkbhjbjhu

PLEASE HELP I GIVE BRAINLIEST I NEED IT ASAP

Answers

Answer:

D 13

Step-by-step explanation:  L+L+W+W=Perimeter

2(1/4x)+2(2x+1)=4.5x+2            

4.5x+2=29        Subtract 2

4.5x=27             Divide by 4.5

x=6                                                            1/4(6)= 1.5 W=1.5      1.5(2)=3

                                                                 2(6)+1=13                  13(2)=26

                                                                                   26+3=29inches perimeter

Answer:

A: 12 4/9

Step-by-step explanation:

1/4x (2x + 1) = 29 (Combine like terms, NOT distributive property!!!)

   2 1/4x + 1 = 29

               - 1    - 1

2 1/4 / 2 1/4x = 28 / 2 1/4

                  x = 12 4/9

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