Being an arithmetic sequence there will be common difference between the consecutive terms

Option A is incorrect because it is not necessary that explicit formula is an arithmetic sequence we can create explicit formula for any sequence

Option B is incorrect because recursive formula can be created for any sequence for geometric series also.

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

Option C is incorrect because the sequence that has constant ratio is the geometric sequence not an arithmetic sequence.

Answer from: irickkadenl

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.

Answer from: ygneely

D

Step-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.

Answer from: iva60

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.”

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