alleryStart learning →Once a sequence is known to be arithmetic, how much subtraction is needed to find the common difference?
AEvery consecutive pair must be subtracted
BOne term subtracted from the next suffices
CThe first and last terms must be subtracted
DAll terms must be subtracted from the first
Answer & Solution
Correct answer: B. One term subtracted from the next suffices
1. Being arithmetic already guarantees that the difference is the same everywhere.
2. So any one term subtracted from the term that follows it gives that shared value.
3. Checking every consecutive pair is what you do to test whether a sequence is arithmetic in the first place, not to measure d once you know it is.
4. Subtracting the first term from the last would give the total change across many steps rather than one step.
_Source: OpenStax Algebra and Trigonometry (CC BY 4.0), Ch 13 "Sequences, Probability and Counting Theory", section 13.2 Arithmetic Sequences_
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