Algebra · Sequences
Chapter 1 · 4
The idea
Geometric, Fibonacci and other special sequences
Why geometric sequences multiply where arithmetic ones add, how Fibonacci-type rules turn into algebra, the named sequences worth recognising on sight, and subscript notation for term-to-term rules.
A full journey — read it, play with it, work it, then earn real exam marks. Everything stays on the timeline below.
In this lesson — start anywhere
Algebra · Sequences
Geometric, Fibonacci and other special sequences
Why geometric sequences multiply where arithmetic ones add, how Fibonacci-type rules turn into algebra, the named sequences worth recognising on sight, and subscript notation for term-to-term rules.
Why it works
Not everything climbs by adding
"Write down the next two terms of " looks like a one-mark gift — and it is, unless you assume every sequence climbs by adding. This one doesn't, and the exam keeps a whole shortlist of favourite "other" rules. Each has a tell, and the first move is always the same: interrogate the gap between neighbours. Is it a constant sum, a constant factor, or the two terms before?Geometric: multiply by a ratio
doubles each time — the next terms are . Spot the ratio by dividing neighbours: . Continuing a geometric sequence by adding the first gap (24 + 3 = 27) is the classic trap — always test whether neighbours differ by a sum or a factor.Keep reading — free
The rest of the explanation, plus 2 worked examples you step through move by move.
Start freeTakes a minute — no card.