# Number patterns

I have a number pattern I need help with.... can someone complete the pattern and explain the process:

700,500; 600,200; 499,900; __________; ___________; _____________

Pattern explain:________________________________________________________ _______________________________________________________________

Everybody looks for patterns in different ways, depending on how their brain works. For me, I always like to start with the simplist strategies and work up from there. So first start out by finding the difference between each set of numbers, you can easily set up a construction of doing this in a triangle method, which I will attempt to demonstrate on a computer, but is easier to do on paper:

$$\begin{multline*} Number 1 \\ (Number 2 - Number1) \\ \end{multline*}$$
$$\begin{multline*} Number 2 \\ (Number 3 - Number2) \\ \end{multline*}$$
$$\begin{multline*} Number 3 \end{multline*}$$

You can then form a new line by doing the same iterative process down the next group of numbers.

The formula then follows that in the first line that you made, there is a linear relation between the variables. (t) The second line corresponds to a (t^2) quadratic relation etc.

If this doesn't work, start looking at ratios and the like looking for different relationships, but I have a feeling that in this case, it will work well.

~Lyuokdea

just as a hint, try thinking about the 499 as 500-1 instead of 499

Tide