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

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]

This is a pretty easy question but I am confused. 6th grade math.
I will give brainliest to right answer!

You know that multiplication can also be expressed as repeated addition. Why is it more difficult to use repeated addition when multiplying two mixed numbers than it is to use repeated addition when you are multiplying a mixed number by a whole number?

What is the explicit formula for this arithmetic sequence?
3,9,15,21,27​

PLEASE I NEED HELP I GIVE BRAINLIEST

Ali can serve 12 customers every 30 minutes, while Alyssa can serve 5 customers in 10 minutes. Who can serve more customers in one hour?
How many more customers can be served in that hour?

On Andrew's note, he wrote that -5 > -10. Which number did he indicate was the greater number?
A. 0°
B. -10°
C. -5°

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Please work out all the problems on this page, no links, no i don't knows please do not take advantage of me or my points please actually answer these questions


tell me step by step

You are conducting an experiment on flipping a coin and picking a letter from the Word SCHOOL. What is the probability of rolling a head or selecting a "C"?

A
50%

B
90%

C
75%

D
67%

4(p-5) = 2p+18 i need all the steps

Describe the function between x=-4 and x=-1

A freight train from city A to city B and a passenger train from city B to city A left the cities at the same time, at 10 am, heading towards each other. The distance between the cities is 360 miles. The freight train is traveling at 50 mph, the passenger train is traveling at 70 mph.

At what time will the trains pass each other?

Write the equation of the line in slope-intercept for using y=mx+b​

How do i distribute this into an equivalent expression? -12(-2+4)

can you help me plssssss

At last, we stopped running. Relief washed over us. Whatever had been chasing us was long gone. We were home and finally safe behind a locked door.

What type of conclusion does the author provide?

(1 point)

The author is reminding readers of the purpose.

The author is stating his or her opinion.

The author is stating his or her feelings.

The author is providing a lesson learned.

Find the nth term of this sequence
2,4,6,8,........

3(-4y+5)-8(-2y-4) can be written in the form (ay+b) by following the following steps:

(Step 1.) distributive property: -12y+15+16y+32

(Step 2) rearranging terms: -12y+16y+15+32

(Step 3) combining like terms: 4y+47

Which step was not done correctly?

A.Step 1

B.Step 2

C.Step 3

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HELP ME PLS I NEED THIS TODAY Juan filled his gas tank four times last week. Here are the amounts of gas he bought (in gallons).
14.1, 4, 18.35, 3.93
What is the total amount of gas Juan bought last week?
show work

What repeated addition equals to 3/4




Good luck シ

Given the following set of data: 3, 4, 5, 6, 8, 9, 9, which measures below have a value of 6? (Check all
that apply.)
O mode
Orange
o high value
O median

Find the area of the figure to the nearest hundredth.
HELP MEH

3(-4y+5)-8(-2y-4) can be written in the form (ay+b) by following the following steps:

(Step 1.) distributive property: -12y+15+16y+32

(Step 2) rearranging terms: -12y+16y+15+32

(Step 3) combining like terms: 4y+47

Which step was not done correctly?

help me solve this please

PLEASE HELP I WILL GIVE BRAINLIEST

Which statement accurately describes the scatterplot

I HAVE POINTS TO GIVE FOR THE FIRST CORRECT PERSON TO AWNSER THESE QUESTIOnS
Find the difference of -4 - (-9) *
Find the difference of -9 - 4 Which expression has the same value as (-14) - (-8)? *
1 point
(-14) + 8
14 - (-8)
14 + (-8)
(-14) + (-8)