imc

The average of two numbers, $a$ and $b$, is defined as $\frac{a+b}{2}$. Thus the average of $x$ and $x^2$ would be $\frac{x(x+1)}{2}$. With that said, we need to find the sum when we plug, $1$, $2$ and $3$ into that equation. So: $$\frac{1(1+1)}{2}+\frac{2(2+1)}{2}+\frac{3(3+1)}{2}=\frac{2}{2}+\frac{6}{2}+\frac{12}{2}=1+3+6=\boxed{10}$$