Answer :
To determine which of the given sequences is an arithmetic sequence, we need to check if the difference between consecutive terms is constant in each sequence. Let's go through each sequence step-by-step:
### Sequence A: \(-48, -24, -12, -6, -3, \ldots\)
First, calculate the differences between consecutive terms:
- \(-24 - (-48) = 24\)
- \(-12 - (-24) = 12\)
- \(-6 - (-12) = 6\)
- \(-3 - (-6) = 3\)
The differences are \(24, 12, 6, 3\). These differences are not the same, hence Sequence A is not an arithmetic sequence.
### Sequence B: \(1, 6, 12, 18, 24, \ldots\)
Next, calculate the differences between consecutive terms:
- \(6 - 1 = 5\)
- \(12 - 6 = 6\)
- \(18 - 12 = 6\)
- \(24 - 18 = 6\)
The first difference is \(5\), and the rest are \(6\). These differences are not the same, hence Sequence B is not an arithmetic sequence.
### Sequence C: \(-2, 6, -10, 14, -18, \ldots\)
Calculate the differences between consecutive terms:
- \(6 - (-2) = 8\)
- \(-10 - 6 = -16\)
- \(14 - (-10) = 24\)
- \(-18 - 14 = -32\)
The differences are \(8, -16, 24, -32\). These differences are not the same, hence Sequence C is not an arithmetic sequence.
### Sequence D: \(-2, -8, -14, -20, -26, \ldots\)
Finally, calculate the differences between consecutive terms:
- \(-8 - (-2) = -6\)
- \(-14 - (-8) = -6\)
- \(-20 - (-14) = -6\)
- \(-26 - (-20) = -6\)
All the differences are \(-6\). These differences are all the same, hence Sequence D is an arithmetic sequence.
### Conclusion
Based on the analysis, the sequence that is an arithmetic sequence is:
- D: [tex]\(-2, -8, -14, -20, -26, \ldots\)[/tex]
### Sequence A: \(-48, -24, -12, -6, -3, \ldots\)
First, calculate the differences between consecutive terms:
- \(-24 - (-48) = 24\)
- \(-12 - (-24) = 12\)
- \(-6 - (-12) = 6\)
- \(-3 - (-6) = 3\)
The differences are \(24, 12, 6, 3\). These differences are not the same, hence Sequence A is not an arithmetic sequence.
### Sequence B: \(1, 6, 12, 18, 24, \ldots\)
Next, calculate the differences between consecutive terms:
- \(6 - 1 = 5\)
- \(12 - 6 = 6\)
- \(18 - 12 = 6\)
- \(24 - 18 = 6\)
The first difference is \(5\), and the rest are \(6\). These differences are not the same, hence Sequence B is not an arithmetic sequence.
### Sequence C: \(-2, 6, -10, 14, -18, \ldots\)
Calculate the differences between consecutive terms:
- \(6 - (-2) = 8\)
- \(-10 - 6 = -16\)
- \(14 - (-10) = 24\)
- \(-18 - 14 = -32\)
The differences are \(8, -16, 24, -32\). These differences are not the same, hence Sequence C is not an arithmetic sequence.
### Sequence D: \(-2, -8, -14, -20, -26, \ldots\)
Finally, calculate the differences between consecutive terms:
- \(-8 - (-2) = -6\)
- \(-14 - (-8) = -6\)
- \(-20 - (-14) = -6\)
- \(-26 - (-20) = -6\)
All the differences are \(-6\). These differences are all the same, hence Sequence D is an arithmetic sequence.
### Conclusion
Based on the analysis, the sequence that is an arithmetic sequence is:
- D: [tex]\(-2, -8, -14, -20, -26, \ldots\)[/tex]
