1. The arithmetic sequence $\left\{a_{n}\right\}$ satisfies $a_{2021}=a_{20}+a_{21}=1$, then the value of $a_{1}$ is $\qquad$
$$
\left\{\begin{array}{l}
a_{1}+2020 d=1, \\
2 a_{1}+39 d=1
\end{array} \Rightarrow(4040-39) a_{1}=2020-39 \Rightarrow a_{1}=\frac{1981}{4001}\right. \text {. }
$$

The translation is as follows:

$$
\left\{\begin{array}{l}
a_{1}+2020 d=1, \\
2 a_{1}+39 d=1
\end{array} \Rightarrow(4040-39) a_{1}=2020-39 \Rightarrow a_{1}=\frac{1981}{4001}\right. \text {. }
$$