MATH COUNTS QUESTION #20

Sum of first $n$ positive odd integers equals $n^2$ .

$9^2=81$

$\begin{aligned} S_n & = \dfrac n2 \{2a + (n-1)d\} \\ & = \dfrac 92 \{2 \cdot 1 + (9-1)2\} ~~~ [ n =9, d= 3-1 =2, a =1] \\ & = \dfrac 92 \cdot 18 \\ & = 9 \cdot 9 \\ & = \boxed{81} \\ \end{aligned}$