Meager information?

This AP starts with a positive odd integer and it only has a single mid term. So, the number of terms in this progression is odd. Mid-term is greater than its first term so the progression is non-constant and the common difference is positive. Its common difference $\equiv (\text{mod 2016})$ indicates that the common difference is an integer divisible by $2016$ . Its not a negative integer as explained before. So, the common difference is a positive even integer because 2016 is even. Since the common difference is a positive integer, the number of terms in this progression is a positive odd number. Now, the last term = $\text{First term} + \left(\text{Number of terms - 1}\right)×\text{Common difference}\\ = \text{Positive odd integer} + \left(\text{Positive odd integer - 1}\right)×\text{Positive even integer}\\ = \text{Positive odd integer} + \left(\text{Non- negative even integer × Positive even integer}\right)\\ = \text{Positive odd integer} + \text{Non - negative even integer}\\ = \color{#69047E}{\boxed{\text{Positive odd integer}}}$

1)It starts with an odd number

2)Only one mid term $\rightarrow$ odd number of terms

3)Mid term is more than starting number $\rightarrow$ increasing AP

4)Common difference is divisible by a even number(2016) $\rightarrow$ common difference must be even

From 1 and 4, all the terms are odd (since, $odd+even=odd$ )

Hence the option, last term is positive odd integer