28. a) Express the $n$-th term of an arithmetic progression in terms of the first term $u_{1}$ and the common difference $d$.

b) Express the $n$-th term of a geometric progression in terms of the first term $u_{1}$ and the common ratio $q$.
28. a) From the definition of an arithmetic progression, we have

$$
\begin{aligned}
u_{n}=u_{n-1}+d=u_{n-2}+2 d & =\ldots= \\
& =u_{1}+(n-1) d
\end{aligned}
$$

b) From the definition of a geometric progression, we have

$$
u_{1}=u_{n-1} q=u_{n-2} q^{2}=\ldots=u_{1} q^{n-1}
$$