  In the first installment of this series, we proved that, for every integer
$a\geq 3$ and every $m\geq 2a^2-a+2$, the 2-color Rado number of $x_1 + x_2 +
\cdots + x_{m-1} = ax_m$ is $\lceil\frac{m-1}{a} \lceil\frac{m-1}{a}
\rceil\rceil$. Here we obtain the best possible improvement of the bound on
$m.$ We prove that if $3|a$ then the 2-color Rado number is
$\lceil\frac{m-1}{a} \lceil\frac{m-1}{a} \rceil\rceil$ when $m\geq 2a+1$ but
not when $m=2a,$ and that if $3\nmid a$ then the 2-color Rado number is
$\lceil\frac{m-1}{a} \lceil\frac{m-1}{a} \rceil\rceil$ when $m\geq 2a+2$ but
not when $m=2a+1.$ We also determine the 2-color Rado number for all $a\geq 3$
and $m\geq \frac{a}{2}+1.$
