1. **Stating the problem:** A pool is being filled with water, and every minute, 8 additional gallons of water are added. We want to find the total amount of water in the pool after a certain number of minutes. 2. **Formula used:** This is an arithmetic sequence where the total amount of water after $n$ minutes is given by: $$a_n = a_1 + (n-1)d$$ where $a_1$ is the initial amount of water, $d$ is the common difference (amount added each minute), and $n$ is the number of minutes. 3. **Important rules:** - The sequence increases by a constant amount each step. - If the pool starts empty, $a_1 = 0$. 4. **Intermediate work:** Assuming the pool starts empty, $a_1 = 0$ and $d = 8$ gallons. So, $$a_n = 0 + (n-1) \times 8 = 8(n-1)$$ This means after $n$ minutes, the pool has $8(n-1)$ gallons of water. 5. **Explanation:** - At minute 1, the pool has $8(1-1) = 0$ gallons (just started). - At minute 2, the pool has $8(2-1) = 8$ gallons. - At minute 3, the pool has $8(3-1) = 16$ gallons, and so on. This formula helps you find the total water after any number of minutes. **Final answer:** The total amount of water in the pool after $n$ minutes is $$a_n = 8(n-1)$$ gallons.