Finite differences

Finite differences is a way of figuring out the difference between two numbers in a sequence. It's like counting how many steps you take to get from one number to the next.

Let's say you have a sequence of numbers: 1, 3, 6, 10, 15. You can find the difference between each number by subtracting the one before it.

For example, to find the difference between 1 and 3, you would do:
3 - 1 = 2. This tells you that it took 2 steps to get from 1 to 3.

Then to find the difference between 3 and 6, you would do:
6 - 3 = 3. This tells you that it took 3 steps to get from 3 to 6.

You can keep doing this for each number in the sequence. When you write out all the differences, you get a new sequence of numbers: 2, 3, 4, 5.

This new sequence is called the finite difference sequence, and it tells you how much the original sequence is changing between each number. You can use this information to make predictions about what the next number in the original sequence might be.

Overall, finite differences is a way of figuring out how things change over time by looking at the differences between each step. It's like counting how many steps you take to get from one point to another, and it can help you understand patterns and make predictions.