Question

Given the arithmetic sequence difference 3/2, 1/2, -1/2 -3/2 ..., find the common difference.

Answer 1

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.

1. Calculate the difference between the first two terms:
\[
\frac{1}{2} - \frac{3}{2} = -\frac{2}{2} = -1
\]

2. Calculate the difference between the second and third terms:
\[
-\frac{1}{2} - \frac{1}{2} = -1
\]

3. 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 \( -1 \).