Dont understand this! Need help from anyone please please! Choose any four consecutive whole numbers. a. multiply the first and last numbers together. multiply the middle pair together. Choose...

Dont understand this! Need help from anyone please please!

Choose any four consecutive whole numbers.

a. multiply the first and last numbers together. multiply the middle pair together. Choose several sets of four consecutive whole numbers and do the same.

b. Make a conjecture based on what you notice in part a.

c. prove/ or disaprove this conjecture for every set of four consecutive whole numbers.

d. what happens if you take four consecutive even numbers and do the same? or four consecutive odd numbers?

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crmhaske's profile pic

Posted on

a)
Choose 4 consecutive whole numbers:1 2 3 4

(1)(4)=4 and (2)(3)=6

Another 4: 2 3 4 5
(2)(5)=10 and (3)(4)=12

Another 4: 3 4 5 6
(6)(3)=18 and (4)(5)=20

b) Following this pattern, the resulting two numbers are separated by 2.

c) In order to prove this:

Let n = number 1
Let n+1 = number 2
Let n+2 = number 3
Let n+4 = number 4

`(n)(n+4)=n^2+4n`
`(n+1)(n+2)=n^2+4n+2`

`(n^2+4n+2)-(n^2+4n)`
`=2`

Therefore, the difference will always be 2

d) Let's try this with even numbers:

Let 2n = number 1
Let 2n+2 = number 2
Let 2n+4 = number 3
Let 2n+6 = number 4

`(2n)(2n+6)=4n^2+12n`
`(2n+2)(2n+4)=4n^2+12n+8`

`(4n^2+12n+8)-(4n^2+12n)`
`=8`

Therefore, the difference will always be 8 when the numbers are consecutive even numbers

Now for odd numbers:

Let 2n+1 = number 1
Let 2n+3 = number 2
Let 2n+5 = number 3
Let 2n+7 = number 4

`(2n+1)(2n+7)=4n^2+16n+7`
`(2n+3)(2n+5)=4n^2+16n+15`

`(4n^2+16n+15)-(4n^2+16n+7)`
`=15-7`
`=8`

Therefore, the difference will always be 8 when the numbers are consecutive odd numbers.

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