1. **State the problem:** We are given the first 4 terms of an arithmetic sequence: 12, 7, 2, -3. We need to find an expression for the nth term of the sequence. 2. **Recall the formula for the nth term of an arithmetic sequence:** $$a_n = a_1 + (n-1)d$$ where $a_n$ is the nth term, $a_1$ is the first term, and $d$ is the common difference. 3. **Find the common difference $d$:** Subtract the first term from the second term: $$d = 7 - 12 = -5$$ 4. **Write the nth term formula using $a_1 = 12$ and $d = -5$:** $$a_n = 12 + (n-1)(-5)$$ 5. **Simplify the expression:** $$a_n = 12 - 5(n-1)$$ $$a_n = 12 - 5n + 5$$ $$a_n = (12 + 5) - 5n$$ $$a_n = 17 - 5n$$ 6. **Check the formula with the first term ($n=1$):** $$a_1 = 17 - 5(1) = 17 - 5 = 12$$ which matches the given first term. **Final answer:** $$\boxed{a_n = 17 - 5n}$$