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]

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

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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)

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What is the total amount of gas Juan bought last week?
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What type of conclusion does the author provide?

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The author is reminding readers of the purpose.

The author is stating his or her opinion.

The author is stating his or her feelings.

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help me solve this please

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

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

What repeated addition equals to 3/4




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Find the area of the figure to the nearest hundredth.
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4(p-5) = 2p+18 i need all the steps

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At what time will the trains pass each other?

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

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?

This is a pretty easy question but I am confused. 6th grade math.
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Describe the function between x=-4 and x=-1

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

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

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