Linear difference equation

Okay kiddo, let's say you have a robot that likes to count. Sometimes, it counts up by one, and other times it counts down by one. We can think of this as a sequence of numbers.

Now, let's say that we want to figure out what the robot will count on the 5th day. We can use a special rule called a difference equation to help us figure it out.

A difference equation is like a special set of instructions that tells us how to find each number in the sequence based on the ones that came before it. In other words, it tells us what the robot will count on each day based on what it counted the day before.

A linear difference equation is a special kind of difference equation where the way the next number is calculated is a straight line. So, if the robot counts up by 3 every day, we would say that the difference equation is linear because the number it counts on any given day is simply a multiple of the day number: 1 x 3, 2 x 3, 3 x 3, and so on.

So, to summarize, a linear difference equation is like a set of instructions that helps us figure out what comes next in a sequence of numbers, and it works by calculating the next number based on the one before it using a straight line.