3.1.3 * Let $\left\{a_{n}\right\}$ be an arithmetic sequence, $a_{1}=19, a_{26}=-1$. Let $A=a_{n}+a_{n+1}+\cdots+a_{n+6}$, where $n$ is a positive integer, find the minimum value of $|A|$.
From $a_{26}=a_{1} + 25d$, we get the common difference $d=-\frac{4}{5}$. In the sequence $\left\{a_{n}\right\}$, the term with the smallest absolute value is $a_{25}=$ $-1-\left(-\frac{1}{5}\right)=\frac{-1}{5}$. $|A|=\left|7 a_{n+3}\right| \geqslant \frac{7}{5}$.
When $n=22$, $|A|=\frac{7}{5}$. Therefore, the minimum value of $|A|$ is $\frac{7}{5}$.