Sequences—Basic elements for discrete mathematics

Sequences are fundamental mathematical objects with a long history in mathematics. Sequences are also tools for the development of other concepts (e. g. the limit concept), as well as tools for the mathematization of real-life situations (e. g. growth processes). But, sequences are also interesting objects in themselves, with lots of surprising properties (e. g. Fibonacci sequence, sequence of prime numbers, sequences of polygonal numbers). Nowadays, new technologies provide the possibility to generate sequences, to create symbolic, numerical and graphical representations, to change between these different representations. Examples of some empirical investigation are given, how students worked with sequences in a computer-supported environment.