1. Problem: Find the 50th term of the sequence defined by $4n+3$ given the 100th term is 403. 2. Formula: The $n^{th}$ term of the sequence is given by $T_n = 4n + 3$. 3. Given $T_{100} = 4(100) + 3 = 400 + 3 = 403$, which matches the problem statement, confirming the formula. 4. To find the 50th term, substitute $n=50$: $$T_{50} = 4(50) + 3 = 200 + 3 = 203$$ 5. Therefore, the 50th term is $203$.