Given the arithmetic sequence 3/2,1/2,−1/2,−3/2, . . .

Question

, find the common difference.(1 point)
The common difference of the arithmetic sequence is d=
.

Answer 1

To find the common difference \( d \) in the arithmetic sequence, we subtract the first term from the second term.

Given the first few terms:

1. First term (\( a_1 \)) = \( \frac{3}{2} \)
2. Second term (\( a_2 \)) = \( \frac{1}{2} \)

The common difference \( d \) can be calculated as follows:

\[ d = a_2 - a_1 = \frac{1}{2} - \frac{3}{2} = \frac{1 - 3}{2} = \frac{-2}{2} = -1 \]

Thus, the common difference of the arithmetic sequence is \( d = -1 \).