# Fiona Has Proved That A Function, F(X), Is An Arithmetic Sequence. How Did She Prove That?

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.

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

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.

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.

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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