What is the common difference between consecutive terms in the following arithmetic sequence?

[tex]\[ 51, 47, 43, 39, \ldots \][/tex]

A. 4
B. 3
C. -4
D. -3



Answer :

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].