1. Given
$$
\begin{array}{l}
(\sqrt{2017} x-\sqrt{2027})^{2017} \\
=a_{1} x^{2017}+a_{2} x^{2016}+\cdots+a_{2017} x+a_{2018} .
\end{array}
$$

Then $\left(a_{1}+a_{3}+\cdots+a_{2017}\right)^{2}-$
$$
\begin{aligned}
& \left(a_{2}+a_{4}+\cdots+a_{2018}\right)^{2} \\
= &
\end{aligned}
$$
$$
\begin{array}{l}
\text { Let } m=a_{1}+a_{3}+\cdots+a_{2017}, \\
n=a_{2}+a_{4}+\cdots+a_{2018} \text {. }
\end{array}
$$

When $x=1$, we get
$$
\begin{array}{l}
m+n=(\sqrt{2017}-\sqrt{2027})^{2017} \text {. } \\
\text { When } x=-1 \text {, we get } \\
m-n=(\sqrt{2017}+\sqrt{2027})^{2017} . \\
\text { Therefore, } m^{2}-n^{2}=(m+n)(m-n) \\
=\left((\sqrt{2017})^{2}-(\sqrt{2027})^{2}\right)^{2017} \\
=-10^{2017} \text {. }
\end{array}
$$