Difference equation

A difference equation is like a recipe that tells you how to make a math sequence.

Let's pretend we're making a line of blocks. We'll start with one block and add two more blocks every time. So our sequence looks like:

1, 3, 5, 7, 9...

We can write a difference equation to show how to get each number in the sequence. The equation looks like this:

y[n] = y[n-1] + 2

Now let's break down what each part of the equation means:

- y[n] is the current number in the sequence we're trying to find
- y[n-1] is the previous number in the sequence
- + 2 means we're adding two to the previous number to get the current one

So to find the third number in our block sequence using the difference equation, we can plug in n = 3:

y[3] = y[2] + 2
y[3] = 5 + 2
y[3] = 7

And there we have it! The third number in our block sequence is 7.

Difference equations are helpful because they let you find any number in a math sequence without having to write out the entire sequence. You can just follow the recipe!