alleryStart learning →What property makes a sequence arithmetic?
AAny term divided by the previous term is constant
BAny term multiplied by its position is constant
CAny term added to the previous term is constant
DAny term minus the previous term is constant
Answer & Solution
Correct answer: D. Any term minus the previous term is constant
1. In an arithmetic sequence the gap between neighbouring terms never changes.
2. That gap is the difference between any two consecutive terms, so subtracting the previous term from a term gives a constant.
3. That constant is called the common difference.
4. A constant quotient of consecutive terms defines a geometric sequence instead, so that option describes a different family.
_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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