Question

What is the common difference of the arithmetic sequence 74, 34, −14, −54,…
?(1 point)
Responses

d=4
d equals 4

d=−1
d equals negative 1

d=1
d equals 1

d=−4

Answer 1

To find the common difference \(d\) of the arithmetic sequence, you subtract any term from the subsequent term.

Let's take the first two terms:

\[
d = 34 - 74 = -40
\]

Now let's check the next pair of terms:

\[
d = -14 - 34 = -48
\]

Let's check the next pair of terms:

\[
d = -54 - (-14) = -40
\]

Therefore, the correct common difference \(d\) is:

\[
d = -40
\]

It appears that there might be a miscommunication regarding the choices you’ve provided, as none of them reflect the correct common difference of -40. Please double-check the sequence or the options given. Based on the provided sequence, the common difference is indeed \(d = -40\).