(22 (12 points) To understand the vision conditions of senior high school students at a certain school, a random check was conducted on the vision conditions of 100 senior high school students, resulting in a frequency distribution histogram as shown. Due to an accident, some data were lost, but it is known that the frequencies of the first 4 groups from left to right are the first four terms of the geometric sequence $\left\{a_{n}\right\}$, and the frequencies of the last 6 groups from left to right are the first six terms of the arithmetic sequence $\left\{b_{n}\right\}$.
(1) Find the general term formula of the geometric sequence $\left\{a_{n}\right\}$;
(2) Find the maximum frequency;
(3) Let $\frac{c_{1}}{a_{1}}+\frac{c_{2}}{a_{2}}+\cdots+\frac{c_{n}}{a_{n}}=b_{n+1}\left(n \in \mathbf{N}^{*}\right)$, find the sum of the first 2007 terms of the sequence $\left\{c_{n}\right\}$, $S_{2007}$.
22 (1) From the problem, we know that $a_{1}=0.1 \times 0.1 \times 100=1, a_{2}=0.3 \times 0.1 \times$ $100=3$. Therefore, the sequence $\left\{a_{n}\right\}$ is a geometric sequence with the first term $a_{1}=1$ and common ratio 3, $a_{n}=3^{n-1}, b_{1}=a_{4}=27$.
Also,
$$
\begin{aligned}
b_{1}+b_{2}+\cdots+b_{6} & =100-\left(a_{1}+a_{2}+a_{3}\right) \\
& =100-(1+3+9) \\
& =87=6 b_{1}+\frac{6 \times 5}{2} d,
\end{aligned}
$$

Solving for $d$ gives $d=-5$. Therefore, the sequence $\left\{b_{n}\right\}$ is an arithmetic sequence with the first term $b_{1}=27$ and common difference -5, $b_{n}=32-5 n$.
(2) The maximum frequency is $\frac{27}{100}=0.27$.
(3) $\frac{c_{n}}{a_{n}}=b_{n+1}-b_{n}=-5$, so $c_{n}=-5 a_{n}=-5 \cdot 3^{n-1}\left(n \in \mathbf{N}^{*}\right.$, $n \geqslant 2)$, and $\frac{c_{1}}{a_{1}}=b_{2}=22, c_{1}=22$, thus the sequence $\left\{c_{n}\right\}$ is a geometric sequence with a common ratio of 3 starting from the 2nd term, $S_{2007}=\frac{5\left(1-3^{2007}\right)}{2}+27$.