To find the common difference of the arithmetic sequence, you subtract the first term from the second term (or any term from the next term).
Let's calculate the common difference \( d \):
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Between the first term (74) and the second term (34): \[ d = 34 - 74 = -40 \]
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Between the second term (34) and the third term (−14): \[ d = -14 - 34 = -48 \]
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Between the third term (−14) and the fourth term (−54): \[ d = -54 - (-14) = -40 \]
Now let's compute the common difference consistently:
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From 74 to 34: \[ d = 34 - 74 = -40 \]
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From 34 to −14: \[ d = -14 - 34 = -48 \]
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From -14 to -54: \[ d = -54 + 14 = -40 \]
It appears there was a mistake in assuming the sequence is arithmetic. The common difference is not consistent among all pairs.
Let’s calculate \( d \) correctly: The common difference is the same for all pairs in a proper arithmetic sequence. The calculations are confirming that this is not a straightforward arithmetic sequence with multiple common differences.
So available responses do not seem to match up with the sequence as described, indicating there may be an error in interpreting or questions. Given the values you provided, the responses as provided don't apply, since the differences calculated do not return a single value recognized as correct based on arithmetic properties.
In the context of your question: None of the answers correctly reflect the consistent common differences calculated. The interpretation of a non-arithmetic series suggests looking beyond standard approaches or re-evaluating the sequence specifics or origin.