ThatKid101
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URGENT! WILL GIVE BRAINLIEST!!
m + b, 2m + b, 3m + b, 4m + b, ... is an infinite sequence. This sequence may be defined in many ways. Which is not a correct way to define this sequence?

A) f(x) = mx + b for x = {1, 2, 3, ...}

B) f(x) = 2m + b + m(x − 2) for x = {1, 2, 3, ...}

C) an = m − b + m(n − 1) for n = {1, 2, 3, ...}

D) a1 = m + b and an + 1 = an + m for n = {1, 2, 3, ...}

Respuesta :

Answer:

Option C) [tex]a_{n}=m-b+m(n-1)[/tex] for [tex]n={\{1,2,3,...}\}[/tex] is not the correct way to define the given infinite sequence

[tex]{\{m+b,2m+b,3m+b,4m+b,...}\}[/tex]

Step-by-step explanation:

Given infinite sequence is [tex]{\{m+b,2m+b,3m+b,4m+b,...}\}[/tex]

Option B) [tex]a_{n}=m-b+m(n-1)[/tex] for [tex]n={\{1,2,3,...}\}[/tex] is not the correct way to define the given infinite sequence [tex]{\{m+b,2m+b,3m+b,4m+b,...}\}[/tex]

Now verify  [tex]a_{n}=m-b+m(n-1)[/tex] for [tex]n={\{1,2,3,...}\}[/tex] is true for the given infinite sequence

That is put n=1,2,3,.. in the above function

[tex]a_{n}=m-b+m(n-1)[/tex]

When n=1,  [tex]a_{1}=m-b+m(1-1)[/tex]

[tex]=m-b+0[/tex]

[tex]a_{1}=m-b\neq m+b[/tex]

When n=2,  [tex]a_{2}=m-b+m(2-1)[/tex]

[tex]=m-b+m[/tex]

[tex]a_{2}=2m-b\neq 2m+b[/tex]

When n=3,  [tex]a_{3}=m-b+m(3-1)[/tex]

[tex]=m-b+2m[/tex]

[tex]a_{3}=3m-b\neq 3m+b[/tex]

and so on.

Therfore [tex]a_{n}=m-b+m(n-1)[/tex] for [tex]n={\{1,2,3,...}\}[/tex] is not the correct way to define the given infinite sequence

[tex]{\{m+b,2m+b,3m+b,4m+b,...}\}[/tex]

Therefore option C) is correct

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