Question

A) Given the arithmetic sequence
3
2
,
1
2
, −
1
2
, −
3
2
, . . . , find the common difference. (1 point)

The common difference of the arithmetic sequence is d =

Answer 1

To find the common difference of the arithmetic sequence, we subtract any term from the subsequent term.

For the given sequence:

- The first term is \( \frac{3}{2} \).
- The second term is \( \frac{1}{2} \).

To find the common difference \( d \):

\[
d = \text{second term} - \text{first term} = \frac{1}{2} - \frac{3}{2}
\]

Calculating this gives:

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

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