Understanding Advanced Sequences
You already know linear sequences (arithmetic sequences) where you add the same number each time, giving you the formula . But what happens when the differences between terms aren't constant?
Quadratic sequences follow the pattern , and they're recognisable because their second differences are always the same. Think of them as sequences that curve rather than go in straight lines.
Here's the key trick: when you find the differences between consecutive terms, then find the differences of those differences, you'll spot a constant pattern. For the sequence 2, 9, 18, 29, 42... the first differences are +7, +9, +11, +13, and the second differences are all +2.
Quick Tip: The second difference divided by 2 always gives you the value of 'a' in your quadratic formula!
