Question

What is the common difference of the arithmetic sequence 74, 34, −14, −54,… ?(1 point) Responses d=−4 d equals negative 4 d=4 d equals 4 d=1 d equals 1 d=−1

Answer 1

To find the common difference of the arithmetic sequence, we can subtract the first term from the second term or the second term from the third term.

Let's calculate it:

1. Subtract the first term (74) from the second term (34):

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

2. Subtract the second term (34) from the third term (−14):

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

3. Subtract the third term (−14) from the fourth term (−54):

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

Thus, the common difference \(d\) for the arithmetic sequence is:

\[
d = -40
\]

It seems that none of the options provided match the calculation. However, if sticking strictly to `common difference` between consecutive terms, use the first two terms to derive the difference:

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

Thus, if this is a mistake and options are correctly transposed. If the choices were meant to explore simple integer workings, and accurate by format in -4/4/etc falls unclear.

Therefore, the common difference \(d\) is \(d = -40\).

Please review the options provided for correctness.