Question 104
Let $a_1, a_2, a_3, a_4, a_5, a_6, a_7$ be distinct positive integers. Find the minimum possible value of $|a_7 - a_1|$ assuming that the sequence $a_1, 2a_2, 3a_3, 4a_4, 5a_5, 6a_6, 7a_7$ is an arithmetic progression. A sequence $x_1, x_2, \dots, x_7$ is called an arithmetic progression if $x_2 - x_1 = x_3 - x_2 = \dots = x_7 - x_6$.