Mathematics, 22.08.2019 05:30 HoneySoft

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.

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Answer from: mooncake9090

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 from: jrfranckowiak

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: Quest

plz yuo

step-by-step explanation:

Answer from: Quest

the correct option is 2.

step-by-step explanation:

according to the given information triangle abc is a right angle triangle with right angle at a. segment ab is 5 and segment ac is 7. point d is on segment bc and angles adb and adc are right angles.

it is given that triangles abd, cad, and cba are similar.

two triangles are similar if their corresponding sides are proportional.

in triangle cba, using pythagoras theorem

$ab^2+ac^2=bc^2$

$ab^2+ac^2=x^2$ )

triangle abd and cba are similar,

$\frac{ab}{bc}=\frac{bd}{ab}$

$ab^2=bc\cdot bd$

$25=bc\cdot bd$ (2)

triangle cad and cba are similar,

$\frac{ac}{bc}=\frac{cd}{ac}$

$ac^2=bc\cdot dc$

$7\times 7=bc\cdot dc$

$49=bc\cdot dc$ )

using (1), (2) and (3), we get

$25+49=x^2$

$74=x^2$

hence proved.

therefore option 2 is correct.

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

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