To find the common difference of the arithmetic sequence, we subtract any term from the subsequent term.
For the given sequence:
- The first term is \( \frac{3}{2} \).
- The second term is \( \frac{1}{2} \).
To find the common difference \( d \):
\[ d = \text{second term} - \text{first term} = \frac{1}{2} - \frac{3}{2} \]
Calculating this gives:
\[ d = \frac{1}{2} - \frac{3}{2} = \frac{1 - 3}{2} = \frac{-2}{2} = -1 \]
Thus, the common difference of the arithmetic sequence is \( d = -1 \).