problem: If the first term of an arithmetic sequence equals the third minus the second, and the fourth term is $8$, what is the first term?
solution: Let $d$ be the common difference.  We told that the first term is equal to the third term minus the second term, so the first term is equal to $d$.  Then the second term is equal to $2d$, the third term is equal to $3d$, and the fourth term is equal to $4d = 8$.  Hence, the first term is $d = \boxed{2}$.