The number of sequences that can be written is infinite since any random list of numbers will do. But some types of sequences are decidedly non-random—one of which being the geometric sequence.

Geometric sequences have a common ratio between their terms. See this visually using a keyboard and a hertz measure in this Bitesize KS3 maths video.

Landmark results in geometry and number theory marked an exciting year for mathematics, at a time when advances in artificial intelligence are starting to transform the subject’s future.