To determine which of the given sequences represents an arithmetic sequence, we should check if the difference between consecutive terms is constant for each sequence.
Here are the steps to solve this problem:
1. First sequence: [tex]\(-5, -7, -10, -14, -19\)[/tex]
- Calculate the differences between consecutive terms:
- [tex]\(-7 - (-5) = -2\)[/tex]
- [tex]\(-10 - (-7) = -3\)[/tex]
- [tex]\(-14 - (-10) = -4\)[/tex]
- [tex]\(-19 - (-14) = -5\)[/tex]
- The differences are not constant. Hence, this sequence is not an arithmetic sequence.
2. Second sequence: [tex]\(1.5, -1.5, 1.5, -1.5\)[/tex]
- Calculate the differences between consecutive terms:
- [tex]\(-1.5 - 1.5 = -3\)[/tex]
- [tex]\(1.5 - (-1.5) = 3\)[/tex]
- [tex]\(-1.5 - 1.5 = -3\)[/tex]
- The differences alternate and are not constant. Hence, this sequence is not an arithmetic sequence.
3. Third sequence: [tex]\(4.1, 5.1, 6.2, 7.2\)[/tex]
- Calculate the differences between consecutive terms:
- [tex]\(5.1 - 4.1 = 1.0\)[/tex]
- [tex]\(6.2 - 5.1 = 1.1\)[/tex]
- [tex]\(7.2 - 6.2 = 1.0\)[/tex]
- The differences are not constant. Hence, this sequence is not an arithmetic sequence.
4. Fourth sequence: [tex]\(-1.5, -1, -0.5, 0\)[/tex]
- Calculate the differences between consecutive terms:
- [tex]\(-1 - (-1.5) = 0.5\)[/tex]
- [tex]\(-0.5 - (-1) = 0.5\)[/tex]
- [tex]\(0 - (-0.5) = 0.5\)[/tex]
- The differences are constant. Hence, this sequence is an arithmetic sequence.
Therefore, the fourth sequence [tex]\(-1.5, -1, -0.5, 0, \ldots\)[/tex] is the arithmetic sequence.
