1. **State the problem:** We are given the first four terms of a sequence: 19, 23, 27, 31. We need to find the formula for the nth term of this sequence. 2. **Identify the type of sequence:** The terms increase by a constant difference. Calculate the difference between consecutive terms: $$23 - 19 = 4$$ $$27 - 23 = 4$$ $$31 - 27 = 4$$ Since the difference is constant (4), this is an arithmetic sequence. 3. **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. 4. **Substitute known values:** $$a_1 = 19$$ $$d = 4$$ So, $$a_n = 19 + (n - 1) \times 4$$ 5. **Simplify the expression:** $$a_n = 19 + 4n - 4 = 4n + 15$$ 6. **Final answer:** The nth term of the sequence is $$a_n = 4n + 15$$ This formula allows you to find any term in the sequence by plugging in the value of $n$.