Let's analyze the sequence [5, 4, 9, 1] to see if it forms an arithmetic sequence and determine the common difference if it does.
1. We need to find the differences between consecutive terms in the sequence.
2. Calculate the first difference:
[tex]\( 4 - 5 = -1 \)[/tex]
3. Calculate the second difference:
[tex]\( 9 - 4 = 5 \)[/tex]
4. Calculate the third difference:
[tex]\( 1 - 9 = -8 \)[/tex]
So, the differences between consecutive terms are:
- First difference: -1
- Second difference: 5
- Third difference: -8
5. For a sequence to be arithmetic, all these differences should be the same. However, in this case:
- The first difference is -1,
- The second difference is 5, and
- The third difference is -8.
Since these differences are not the same, the sequence [5, 4, 9, 1] does not have a common difference, meaning it is not an arithmetic sequence.
So, the answer is that there is no common difference in the given sequence [5, 4, 9, 1]. The sequence is not arithmetic.
