An arithmetic sequence is defined by having a constant difference between consecutive terms. In the sequence you provided: \( \frac{3}{2}, \frac{1}{2}, -\frac{1}{2}, -\frac{3}{2} \), we can determine the common difference by subtracting subsequent terms.
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Calculate the difference between the first two terms: \[ \frac{1}{2} - \frac{3}{2} = -\frac{2}{2} = -1 \]
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Calculate the difference between the second and third terms: \[ -\frac{1}{2} - \frac{1}{2} = -1 \]
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Calculate the difference between the third and fourth terms: \[ -\frac{3}{2} - (-\frac{1}{2}) = -\frac{3}{2} + \frac{1}{2} = -\frac{3}{2} + \frac{2}{2} = -\frac{1}{2} \]
The differences, as calculated, are:
- Between 1st and 2nd: \( -1 \)
- Between 2nd and 3rd: \( -1 \)
- Between 3rd and 4th: \( -1 \)
As we can see from the calculations, the common difference of this arithmetic sequence is: \[ -1 \]
Thus, the common difference is \( -1 \).