3. Given an arithmetic sequence $a_{1}, a_{2}, \cdots, a_{1000}$, the sum of the first 100 terms is 100, and the sum of the last 100 terms is 1000. Then $a_{1}=$ $\qquad$
3.0. 505 .

Let the common difference of the arithmetic sequence be $d$. Then
$$
\begin{array}{l}
100 a_{1}+4950 d=100, \\
100 a_{1}+94950 d=1000 .
\end{array}
$$

Therefore, $d=0.01, a_{1}=1-0.495=0.505$.