Video narration
Why does 3, 7, 11, 15 feel like skip-counting, and what makes it an arithmetic progression? Look at the jumps: plus four, plus four, plus four. Each new term comes from the same-sized step. That repeated step is the key-not simply the fact that the numbers go up. This constant gap is called the common difference, written d. Here, d equals four. It can also be negative when the sequence decreases, or zero when every term stays the same. Use the nth-term formula, an = a + (n − 1)d: a is the first term, n is the position, and d is the repeated jump. The fifth term is 3 + (5 − 1) times 4, or 19. Now test 2, 5, 9, 14. Its gaps are 3, 4, and 5, so the jumps change. It fails. So why is 3, 7, 11, 15 an arithmetic progression? Because every next term is made by adding the same number-the common difference.