Question

Given the arithmetic sequence 32,12,−12,−32, . . .
, find the common difference.(1 point)
The common difference of the arithmetic sequence is d=
.
Remaining Attempts : 3

Answer 1

To find the common difference \( d \) of the arithmetic sequence, we subtract any term from the term that follows it.

Let's take the first two terms:

- The first term is \( 32 \).
- The second term is \( 12 \).

Now, we can find the common difference \( d \):

\[
d = 12 - 32 = -20
\]

We can check this with the next two terms as well:

- The second term is \( 12 \).
- The third term is \( -12 \).

Calculating the difference:

\[
d = -12 - 12 = -24
\]

And again with the third and fourth terms:

- The third term is \( -12 \).
- The fourth term is \( -32 \).

Calculating the difference:

\[
d = -32 - (-12) = -32 + 12 = -20
\]

So, the common difference of the arithmetic sequence is \( d = -20 \).