1. **Stating the problem:** Calculate the value of the sum $$\sum_{n=1}^{25} (9n - 8)$$. 2. **Formula and rules:** The sum of a sequence $$\sum_{n=1}^N a_n$$ where $$a_n$$ is an arithmetic expression can be split and summed separately: $$\sum_{n=1}^N (an + b) = a \sum_{n=1}^N n + b \sum_{n=1}^N 1 = a \frac{N(N+1)}{2} + bN$$ 3. **Apply the formula:** Here, $$a=9$$, $$b=-8$$, and $$N=25$$. Calculate $$\sum_{n=1}^{25} n = \frac{25 \times 26}{2} = 325$$. Calculate $$\sum_{n=1}^{25} 1 = 25$$. 4. **Substitute values:** $$\sum_{n=1}^{25} (9n - 8) = 9 \times 325 - 8 \times 25$$ 5. **Calculate each term:** $$9 \times 325 = 2925$$ $$8 \times 25 = 200$$ 6. **Final sum:** $$2925 - 200 = 2725$$ **Answer:** The value of the sum is **2725**.