Example 2. Given the sequence $2,4,9,17,28,42$, $\cdots$, find its general term.

Analysis: If the method of undetermined coefficients is used, a system of six linear equations needs to be solved; if the method of observation and induction is used, it is also quite difficult. If the method of successive differences is adopted—by subtracting the previous term from the next term in the original sequence to obtain a new sequence, and continuing this process, an arithmetic or geometric sequence can eventually be obtained, thus transforming the problem into finding the general term and sum of an arithmetic or geometric sequence.
The difference sequence $\left\{\mathrm{b}_{\mathrm{A}}\right\}$ of the sequence $\left\{\mathrm{a}_{\mathrm{A}}\right\}$ is: $2,5,8,11,14, \cdots$. It is an arithmetic sequence with the first term $2$ and common difference $3$. Therefore,
$$
\begin{array}{l}
b_{n}=2+(n-1) \times 3=3 n-1 \text {. } \\
\text { Hence } a_{n}=a_{1}+\sum_{i=1}^{n-1} b_{i}=\frac{1}{2}\left(3 n^{2}-5 n+6\right) \text {. }
\end{array}
$$