Find the sum of the first 25 odd numbers, 1 + 3 + 5 + …. What do you notice about the answer?

Step 1. The numbers. $a = 1$, $d = 2$, $n = 25$.

Step 2. The formula. $S_{25} = \dfrac{25}{2}[2 + 24 \times 2] = \dfrac{25}{2} \times 50 = 625$.

Step 3. Notice. $625 = 25^2$. In general $S_n = \dfrac{n}{2}[2 + 2(n - 1)] = n^2$.