3. If the sum of the terms of the infinite geometric sequence $\left\{a_{n}\right\}$ is 1, and the sum of the absolute values of the terms is 2, then the value of the first term $a_{1}$ is . $\qquad$
Let the common ratio of the sequence $\left\{a_{n}\right\}$ be $q$. According to the problem, $\left\{\begin{array}{l}\frac{a_{1}}{1-q}=1, \\ \frac{\left|a_{1}\right|}{1-|q|}=2 .\end{array}\right.$ Clearly, $-1<q<1$ and $q \neq 0 \Rightarrow \frac{2 a_{1}}{1-q}=\frac{a_{1}}{1-|q|} \Rightarrow 2|q|-q=1 \Rightarrow q=-\frac{1}{3}, a_{1}=\frac{4}{3}$. Therefore, the first term $a_{1}$ is $\frac{4}{3}$.