Answer:
C) an = m − b + m(n − 1) for n = {1, 2, 3, ...}
Step-by-step explanation:
Nevermind you dont gotta tell me nothin. I just guessed and got C right. lol.
Answer:
Option C
Step-by-step explanation:
It is given that (m + b), (2m + b), (3m + b), (4m + b)...... is an infinite sequence.
To check the correct way to define the sequence we will check each option given.
Option A.
f(x) = mx + b, x = {1, 2, 3.....}
So the sequence formed by placing x = {1, 2, 3.....}
f(1) = m + b
f(2) = 2m + b
So this option is not the answer.
Option B.
f(x) = 2m + b + m(x - 2) for x = {1, 2, 3,........}
f(1) = 2m + b + m(1 - 2)
= 2m + b - m
= m + b
Which is our sequence.
Therefore, this option is not correct.
Option C.
[tex]a_{n}=m-b+m(n-1)[/tex] for n = {1, 2, 3, ........}
[tex]a_{1}=m-b+m(1-1)[/tex]
= m - b
Which is not our sequence.
Therefore, this is the correct option which is not the correct way to define the given sequence.
Option D.
[tex]a_{1}=m+b[/tex] and [tex]a_{n+1}=a_{n}+m[/tex] for n = {1, 2, 3......}
[tex]a_{2}=a_{1}+m[/tex]
= m + b + m
= 2m + b
So, this option is also incorrect.
Therefore, Option C is the answer.
