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Fiona has proved that a function, f(x), is an arithmetic sequence. how did she prove that?

Fiona has proved that a function, f(x), is an arithmetic sequence. how did she prove that? she showed that an explicit formula could be created. she showed that a recursive formula could be created. she showed that f(n) ÷ f(n − 1) was a constant ratio. she showed that f(n) − f(n − 1) was a constant difference.
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4 Answers

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Dr. Juanita Wolff

Feb 20, 2025

The defining characteristic of any arithmetic sequence is called the common difference.  It is a constant difference found between any term and the term preceding it."She showed that f(n)-f(n-1) was a constant difference."... Show More
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Dr. Juanita Wolff

Feb 20, 2025

D. She showed that f(n) - f(n - 1) was a constant difference.Step-by-step explanation:∵ A sequence is called arithmetic if there is constant difference between consecutive numbers,Thus, option D is correct.In Explicit formulas, we define each term in a sequence directly,Thus, there are many sequences other than arithmetic that have explicit formula,i.e. Option A can not be true.Now, recursive formula defines the relation between successive terms,Thus, there are many sequences other than arithmetic that have recursive formula,i.e. Option B can not be true.Also, if the ratio between successive terms is constant then the sequence is a Geometric sequence,A GP can not be an AP,i.e. Option D can not be true.... Show More
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Dr. Juanita Wolff

Feb 20, 2025

DStep-by-step explanation:She showed that f(n) - f(n - 1) was a constant difference. The definition of an arithmetic sequence is the difference between consecutive terms is constant, aka common difference.... Show More
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Dr. Juanita Wolff

Feb 20, 2025

Option D is correctStep-by-step explanation:Option D is correctBeing an arithmetic sequence there will be common difference between the consecutive termsOption A is incorrect because it is not necessary that explicit formula is an arithmetic sequence we can create explicit formula for any sequenceOption B is incorrect because recursive formula can be created for any sequence for geometric series also.Option C is incorrect because the sequence that has constant ratio is the geometric sequence not an arithmetic sequence.... Show More
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