1. **State the problem:** We need to find the total number of seats in a theater with 15 rows, where the first row has 25 seats and each successive row has 2 more seats than the previous one. 2. **Identify the sequence type:** This is an arithmetic sequence where the first term $a_1 = 25$ and the common difference $d = 2$. 3. **Formula for the nth term:** The number of seats in the $n^{th}$ row is given by: $$a_n = a_1 + (n-1)d$$ 4. **Calculate the number of seats in the 15th row:** $$a_{15} = 25 + (15-1) \times 2 = 25 + 14 \times 2 = 25 + 28 = 53$$ 5. **Formula for the sum of the first n terms:** The total number of seats is the sum of all rows: $$S_n = \frac{n}{2} (a_1 + a_n)$$ 6. **Calculate the total seats:** $$S_{15} = \frac{15}{2} (25 + 53) = \frac{15}{2} \times 78$$ 7. **Simplify the multiplication:** $$S_{15} = 15 \times 39 = 585$$ **Final answer:** The theater has **585** seats in total.