KöMaL 2008 B4134

Let $t_3(a_1,\ldots,a_k)$ denote the number of three term arithmetic progressions that can be selected from the terms of a sequence $a_1$<$a_2$<...<$a_k$. Prove that $t_3(a_1,\ldots,a_k)\le t_3(1,2,\ldots,k)$.