CWMO 2015 Problem 6

For a sequence $a_1,a_2,...,a_m$ of real numbers, define the following sets $$A=\{a_i | 1\leq i\leq m\}\ \text{and} \ B=\{a_i+2a_j | 1\leq i,j\leq m, i\neq j\}$$ Let $n$ be a given integer, and $n>2$ . For any strictly increasing arithmetic sequence of positive integers, determine, with proof, the minimum number of elements of set $A\triangle B$ , where $A\triangle B$ $= \left(A\cup B\right) \setminus \left(A\cap B\right).$