  In 1982, Beutelspacher and Brestovansky proved that for every integer $m\geq
3,$ the 2-color Rado number of the equation $$x_1+x_2+...+x_{m-1}=x_m$$ is
$m^2-m-1.$ In 2008, Schaal and Vestal proved that, for every $m\geq 6,$ the
2-color Rado number of $$x_1+x_2+...+x_{m-1}=2x_m$$ is $\lceil
\frac{m-1}{2}\lceil\frac{m-1}{2}\rceil\rceil.$ Here we prove that, for every
integer $a\geq 3$ and every $m\geq 2a^2-a+2$, the 2-color Rado number of
$$x_1+x_2+...+x_{m-1}=ax_m$$ is
$\lceil\frac{m-1}{a}\lceil\frac{m-1}{a}\rceil\rceil.$ For the case $a=3,$ we
show that our formula gives the Rado number for all $m\geq 7,$ and we determine
the Rado number for all $m\geq 3.$
