1. **State the problem:** Find the sum of the first 10 terms, $S_{10}$, of the arithmetic series $3 + 7 + 11 + \dots$. 2. **Identify the first term and common difference:** The first term $a_1 = 3$. The common difference $d = 7 - 3 = 4$. 3. **Formula for the sum of the first $n$ terms of an arithmetic series:** $$S_n = \frac{n}{2} (2a_1 + (n-1)d)$$ 4. **Substitute the known values:** $$S_{10} = \frac{10}{2} (2 \times 3 + (10-1) \times 4)$$ 5. **Simplify inside the parentheses:** $$2 \times 3 = 6$$ $$(10-1) = 9$$ $$9 \times 4 = 36$$ So, $$S_{10} = 5 (6 + 36)$$ 6. **Add inside the parentheses:** $$6 + 36 = 42$$ 7. **Multiply:** $$S_{10} = 5 \times 42 = 210$$ **Final answer:** $S_{10} = 210$ which corresponds to option C.