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.
  for n = {1, 2, 3, ........}
 for n = {1, 2, 3, ........}

     = 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.
 and
 and  for n = {1, 2, 3......}
 for n = {1, 2, 3......}

     = m + b + m 
     = 2m + b
So, this option is also incorrect.
Therefore, Option C is the answer.