1. **State the problem:** Find the sum of all odd numbers from 1 to 50. 2. **Identify the sequence:** The odd numbers from 1 to 50 are 1, 3, 5, ..., 49. 3. **Count the terms:** The number of odd numbers from 1 to 49 is given by $n = \frac{49 - 1}{2} + 1 = 25$. 4. **Use the formula for the sum of an arithmetic sequence:** $$S_n = \frac{n}{2} (a_1 + a_n)$$ where $a_1$ is the first term and $a_n$ is the last term. 5. **Substitute values:** $$S_{25} = \frac{25}{2} (1 + 49) = \frac{25}{2} \times 50$$ 6. **Calculate the sum:** $$S_{25} = 25 \times 25 = 625$$ **Final answer:** The sum of all odd numbers from 1 to 50 is $625$.