Example 1. Write the general term formula for the following sequences:
(1) $1,2,2,3,3,3,4,4,4,4, \cdots, a_{n}, \cdots$;
(2) $1,1,2,2,2,3,3,3,3, \cdots, b_{n}, \cdots$,
(3) $1,1,1,2,2,2,2, \cdots, c_{n} \cdots$.
It is clear that their general term formulas are respectively
$$
\begin{array}{c}
a_{n}=\left[\frac{1+\sqrt{8 n-7}}{2}\right], \\
b_{n}=\left[\frac{-1+\sqrt{8 n+1}}{2}\right], C_{n}=[\sqrt{n}] .
\end{array}
$$