1. In the arithmetic sequence $\left\{a_{n}\right\}$, $a_{9}+a_{10}=a, a_{19}+a_{20}=b, a_{99}+a_{100}=$
1. $9 b-8 a$.
$\left\{a_{n}\right\}$ is an arithmetic sequence, $b_{n}=a_{n}+a_{n+1}$ is also an arithmetic sequence, and $b_{9}=a, b_{19}=b$. Similarly, $b_{9}, b_{19}, b_{29}, \cdots$, $b_{99}$ also form an arithmetic sequence, $b_{99}=b_{9}+9\left(b_{19}-b_{9}\right)=a+9(b-a)=9 b-8 a$, that is, $a_{99}+a_{100}=9 b-8 a$.