CN-TST 2017 Problem 25

Given $n\ge 3$ . consider a sequence $a_1,a_2,...,a_n$ , if $(a_i,a_j,a_k)$ with i+k=2j (i<j<k) and $a_i+a_k\ne 2a_j$ , we call such a triple a $NOT-AP$ triple. If a sequence has at least one $NOT-AP$ triple, find the least possible number of the $NOT-AP$ triple it contains.