Question

Fiona has proved that a function, f(x), is an arithmetic sequence. How did she prove that? A. She showed that an explicit formula could be created. B. She showed that a recursive formula could be created. C. She showed that f(n) ÷ f(n - 1) was a constant ratio. D. She showed that f(n) - f(n - 1) was a constant difference.

Answer 1

Answer:

Option D is correct

Step-by-step explanation:

Option D is correct

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.

Answer 2

Answer:

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.