Example 2. Find the general term formula of the sequences
(1) $1,3,3,5,5,5,7,7,7,7, \cdots, a_{n}, \cdot \cdot$
( 2 ) $2,2,5,5,5,8,8,8,8, \cdots, b_{n} \cdots$
$$
\begin{array}{l}
a_{n}=2\left[\frac{1+\sqrt{8 n-7}}{2}\right]-1, \\
b_{n}=3\left[\frac{-1+\sqrt{8 n+1}}{2}\right]-1 .
\end{array}
$$