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?
An arithmetic sequence is a sequence of numbers where each term is obtained by adding a fixed constant to the previous term. Let's call this constant $d$, and let $a$ be the first term of the sequence. Then, the second term is $a + d$, the third term is $a + 2d$, and the fourth term is $a + 3d$. The problem says that the first term equals the third minus the second, so we can write an equation: $a = (a + 2d) - (a + d)$. Simplifying this equation, we get $a = d$. The problem also says that the fourth term is $8$, so we can write another equation: $a + 3d = 8$. Since $a = d$, we can substitute $a$ for $d$ in this equation and get $4a = 8$. Solving for $a$, we get $a = 2$. Therefore, the first term of the sequence is $2$.

