Example 4. Given $a_{1}=a, a_{n+1}=a_{n}+b_{n}$ (where $b_{n}$ is given as a function of $n$), try to find the general term $a_{n}$.


Given: $| a_{n+1}-a_{n}=b_{n} |$, we know that the general term of the difference sequence is $b_{n}$. Therefore, its general term is
$$
a_{n}=a+\sum_{k=1}^{n-1} b_{k}
$$
N. $a_{n+1}=p a_{i}+d$, the difference sequence is a geometric sequence with a common ratio of $p$.