1. **Problem:** If the $100^{th}$ term of the sequence defined by $4n+3$ is 403, find the $50^{th}$ term. 2. **Formula:** The $n^{th}$ term of the sequence is given by: $$a_n = 4n + 3$$ 3. **Step 1:** Verify the $100^{th}$ term: $$a_{100} = 4 \times 100 + 3 = 400 + 3 = 403$$ This matches the given term, so the formula is correct. 4. **Step 2:** Find the $50^{th}$ term using the formula: $$a_{50} = 4 \times 50 + 3 = 200 + 3 = 203$$ 5. **Answer:** The $50^{th}$ term is **203**.