1. **State the problem:** Evaluate the sum $$\sum_{k=0}^4 (3k - 2)$$. 2. **Recall the formula:** The sum of a sequence $$\sum_{k=a}^b f(k)$$ is the sum of the values of the function $$f(k)$$ for each integer $$k$$ from $$a$$ to $$b$$. 3. **Apply the sum:** Here, $$f(k) = 3k - 2$$, and $$k$$ runs from 0 to 4. 4. **Calculate each term:** $$ 3(0) - 2 = -2 \\ 3(1) - 2 = 1 \\ 3(2) - 2 = 4 \\ 3(3) - 2 = 7 \\ 3(4) - 2 = 10 $$ 5. **Sum the terms:** $$ -2 + 1 + 4 + 7 + 10 = 20 $$ 6. **Alternative method using sum formulas:** $$ \sum_{k=0}^4 (3k - 2) = 3 \sum_{k=0}^4 k - 2 \sum_{k=0}^4 1 $$ 7. **Calculate each sum:** $$ \sum_{k=0}^4 k = 0 + 1 + 2 + 3 + 4 = 10 $$ $$ \sum_{k=0}^4 1 = 5 $$ 8. **Substitute back:** $$ 3 \times 10 - 2 \times 5 = 30 - 10 = 20 $$ **Final answer:** $$\boxed{20}$$