1. **State the problem:** Find the sum of the arithmetic series starting with 25, 22, 19, ... up to the 22nd term. 2. **Identify the series type and formula:** This is an arithmetic series where each term decreases by a constant difference. The formula for the sum of the first $n$ terms of an arithmetic series is: $$S_n = \frac{n}{2} (2a + (n-1)d)$$ where $a$ is the first term, $d$ is the common difference, and $n$ is the number of terms. 3. **Find the common difference $d$:** $d = 22 - 25 = -3$ 4. **Plug in the values:** $a = 25$, $d = -3$, $n = 22$ $$S_{22} = \frac{22}{2} (2 \times 25 + (22 - 1)(-3))$$ 5. **Simplify inside the parentheses:** $$2 \times 25 = 50$$ $$(22 - 1) = 21$$ $$21 \times (-3) = -63$$ So, $$S_{22} = 11 (50 - 63) = 11 (-13)$$ 6. **Calculate the sum:** $$S_{22} = -143$$ **Final answer:** The sum of the first 22 terms of the series is $-143$.