2010 AMC 10B Problems/Problem 4

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:

$\frac{1(1+1)}{2} + \frac{2(2+1)}{2} + \frac{3(3+1)}{2} = \frac{2}{2} + \frac{6}{2} + \frac{12}{2} = 1+3+6= \boxed{\mathrm{(C)} \text{ or } 10}$ .

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2010 AMC 10B Problems/Problem 4