1. **State the problem:** Find the first three terms of the sequence defined by the nth term formula $a_n = 3n + 1$. 2. **Formula used:** The nth term of the sequence is given by $a_n = 3n + 1$, where $n$ is the term number. 3. **Calculate the first term ($n=1$):** $$a_1 = 3(1) + 1 = 3 + 1 = 4$$ 4. **Calculate the second term ($n=2$):** $$a_2 = 3(2) + 1 = 6 + 1 = 7$$ 5. **Calculate the third term ($n=3$):** $$a_3 = 3(3) + 1 = 9 + 1 = 10$$ 6. **Final answer:** The first three terms of the sequence are $4$, $7$, and $10$.