For the $AP: \frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots,$ write the first term $a$ and the common difference $d$.

(N/A) The given arithmetic progression $(AP)$ is $\frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2}, \ldots$
The first term $a$ is the first number in the sequence,so $a = \frac{3}{2}$.
The common difference $d$ is calculated by subtracting any term from the term that follows it,i.e.,$d = a_2 - a_1$.
Substituting the values,$d = \frac{1}{2} - \frac{3}{2} = \frac{1 - 3}{2} = \frac{-2}{2} = -1$.
Thus,the first term $a = \frac{3}{2}$ and the common difference $d = -1$.