Question 3
Suppose that $s_1,s_2,s_3, \dotsc$ is a strictly increasing sequence of positive integers such that the sub-sequences $s_{s_1}$, $s_{s_2}$, $s_{s_3}$, … and $s_{s_1 + 1}$, $s_{s_2 + 1}$, $s_{s_3 + 1}$, … are both arithmetic progressions. Prove that the sequence $s_1$, $s_2$, $s_3$, … is itself an arithmetic progression.