To determine the common difference in an arithmetic sequence, we need to subtract any term from the term that immediately precedes it. In this sequence, the terms are [tex]\(51, 47, 43, 39, \ldots\)[/tex].
Let's find the differences between consecutive terms:
1. Subtract the second term from the first term:
[tex]\[
47 - 51 = -4
\][/tex]
2. Subtract the third term from the second term:
[tex]\[
43 - 47 = -4
\][/tex]
3. Subtract the fourth term from the third term:
[tex]\[
39 - 43 = -4
\][/tex]
Each of these differences is [tex]\(-4\)[/tex], which indicates that the sequence decreases by 4 each time we move to the next term.
Therefore, the common difference in this arithmetic sequence is [tex]\(-4\)[/tex].
The correct answer is [tex]\(\boxed{-4}\)[/tex].
