To find the common difference \( d \) of the arithmetic sequence, we subtract any term from the term that follows it.
Let's take the first two terms:
- The first term is \( 32 \).
- The second term is \( 12 \).
Now, we can find the common difference \( d \):
\[ d = 12 - 32 = -20 \]
We can check this with the next two terms as well:
- The second term is \( 12 \).
- The third term is \( -12 \).
Calculating the difference:
\[ d = -12 - 12 = -24 \]
And again with the third and fourth terms:
- The third term is \( -12 \).
- The fourth term is \( -32 \).
Calculating the difference:
\[ d = -32 - (-12) = -32 + 12 = -20 \]
So, the common difference of the arithmetic sequence is \( d = -20 \).