(In reply to re: My revised solution
by Dej Mar)
Both of us understand the problem and I do not flatly disagree with you. However when you are given 3 numbers like 1,2,3... it is more logical that the next number is 4, although 1,2,3..might be followed by 624 (a(n)= 6*(n-1)*(n-2)*(n-3)+n) or any other number.
Given a=2016 we see a single number, given a couple 1007,1009,..we may guess 1007,1009,1012,1016 or else (including arithm. seq.).
In our case 36 is unacceptable as answer, 35 might be accepted since we know that d=2 is here to stay, and 34 is the most logical (imho), given due explanation.
I revert to my 1st sentence, both of us understand what counts and both approaches are acceptable once justified,