What is an Arithmetic Progression | A-Level Maths?

An arithmetic progression is just a list of numbers that go up or down by the same amount each time.

Imagine you're stacking blocks. You start with 2 blocks on the first step, then add 3 more for the next step, now you have 5 blocks. For the third step, you add another 3, now you have 8 blocks. If you keep adding 3 every time, your steps will look like this: 2, 5, 8, 11, 14... and so on. This is an arithmetic progression, because each number increases by the same amount, in this case, +3.

In an arithmetic progression:

• The first number is called the first term.
• The amount you add or subtract each time is called the common difference.

So if your first term is 2 and your common difference is 3, then every step you take adds 3 more blocks, just like climbing a staircase with evenly spaced steps! You can even count how many blocks you’ll have on any step by multiplying the common difference by the number of steps you’ve taken and adding it to the first term. It's all about pattern and pacing, just like counting your footsteps as you walk home from school.