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3 years ago

Use inductive reasoning to describe the pattern. Then find the next two numbers in the pattern. –9, –4, 1, 6, . . .

Mathematics

2 answers:

Basile [38]3 years ago

7 0

<h3>Answer with Step-by-step explanation:</h3>

We are given a pattern:

-9 , -4 , 1 , 6 , ...

We have to describe the pattern and find the next two terms

-9+5= -4

-4+5= 1

1+5= 6

Hence, the numbers are found by adding five to the previous term

The next two numbers are found as:

6+5 =11

11+5 = 16

Hence, next two numbers are:

11 and 16

Vilka [71]3 years ago

3 0

The pattern is +5 so the next two would be, 11,16

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Bumek [7]

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Step-by-step explanation:

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3 years ago

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Find the generating function for the sequence 1,1,1,2,3,4,5,6,....

marin [14]

Answer:

$P(x)=\dfrac{1}{1-x}+\dfrac{x^3}{(1-x)^2} \quad \text{for} \mid x \mid < 1$ [/tex]

Step-by-step explanation:

The generating function of a sequence is the power series whose coefficients are the elements of the sequence. For the sequence

$1,1,1,2,3,4,5,6,...$

the generating function would be

$P(x)=1+x+x^2+2x^3+3x^4+4x^5+5x^6+...\\$

we can multiply P(x) by x to get

$xP(x)=x+x^2+x^3+2x^4+3x^5+4x^6+...$

Note that

$P(x)-xP(x)=1+(2x^3-x^3)+(3x^4-2x^4)+(4x^5-3x^5)+(5x^6-4x^6)+...\\ \\=1+x^3+x^4+x^5+x^6+...=1+x^3(1+x+x^2+x^3+x^4+...)$

which for $\mid x \mid < 1$ can be rewritten as

$(1-x)P(x)=1+\dfrac{x^3}{(1-x)} \quad \Rightarrow \\\\P(x)=\dfrac{1}{(1-x)}+\dfrac{x^3}{(1-x)^2}$

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3 years ago

If Wayne buys a motorcycle for $8000. Each year the motorcycle loses 20% of its value from the previous year. How much is the mo

nexus9112 [7]

20/100 x 8000 = 1600
1600 x 3 = 4800
8000 - 4800 = 3200

The motorcycle is worth $3,200 after three years.

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8 is 20% of what number

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