1. **State the problem:** Find the sum of the arithmetic series starting with 25, 22, 19, ... up to the 22nd term. 2. **Identify the first term and common difference:** The first term $a_1 = 25$. The common difference $d = 22 - 25 = -3$. 3. **Formula for the $n$th term of an arithmetic sequence:** $$a_n = a_1 + (n-1)d$$ 4. **Find the 22nd term:** $$a_{22} = 25 + (22-1)(-3) = 25 + 21 \times (-3) = 25 - 63 = -38$$ 5. **Formula for the sum of the first $n$ terms of an arithmetic series:** $$S_n = \frac{n}{2}(a_1 + a_n)$$ 6. **Calculate the sum of the first 22 terms:** $$S_{22} = \frac{22}{2}(25 + (-38)) = 11 \times (-13) = -143$$ **Final answer:** The sum of the first 22 terms is $-143$.