Find the sum of the **first $50$ positive odd integers**: $1, 3, 5, 7, \ldots, 99$.

This is an arithmetic series with $a_{1} = 1$, $d = 2$, $n = 50$. The $50$th odd integer: $a_{50} = 1 + 49 \cdot 2 = 99$. Sum: $S_{n} = \dfrac{n}{2}(a_{1} + a_{n}) = \dfrac{50}{2}(1 + 99) = 25 \cdot 100 = 2{,}500$. There's a beautiful identity: the sum of the first $n$ positive odd integers is exactly $n^{2}$. For $n = 50$: $50^{2} = 2{,}500$ ✓. - Trap A is the last term, not the sum. - Trap B ($1275 = 50 \cdot 51 / 2$) is the sum of the first 50 positive integers ($1, 2, 3, \ldots, 50$). - Trap D doubles the answer.