# Weird consecutive numbers question...

• Mar 28th 2008, 05:41 PM
clarebear14
Weird consecutive numbers question...
Take 3 consecutive numbers, e.g. 5,6,7.

• Square each one.
• Subtract 2 from the sum.
• Divide the result by 3.
• Write down number.

• Take 3 other consecutive numbers 10, 11, 12 & repeat.

• Predict answer for 19, 20, 21.

• Using n, n+1, n+2 simplify and show how this pattern works.
(Worried)
• Mar 28th 2008, 06:28 PM
Pterid
Hi,

How far have you got with this question - what part are you looking for help with?
• Mar 28th 2008, 07:27 PM
TheEmptySet
Quote:

Originally Posted by clarebear14
[*]Using n, n+1, n+2 simplify and show how this pattern works.[/LIST](Worried)

adding the three numbers we get

$\displaystyle n^2+(n+1)^2+(n+2)^2 \iff n^2+n^2+2n+1+n^2+4n+4$

$\displaystyle 3n^2+6n+5$ Now subtract 2

$\displaystyle 3n^2+6n+5-2 = 3n^2+6n+3=3(n^2+2n+1)=3(n+1)^2$

Now divide by 3

$\displaystyle \frac{3(n+1)^2}{3}=(n+1)^2$

So we get the square of of the second #. Yeah :D