What do I need to know about recurrence relations?
- A recurrence relation describes each term in a progression as a function of the previous term – ie un+1 = f(un)
- Along with the first term of the sequence, this allows you to generate the sequence term by term
- Both arithmetic progressions and geometric progressions can be defined using recurrence relations
- Arithmetic can be defined by
- Geometric can be defined by
- However, you can also define progressions that are neither arithmetic nor geometric
- For arithmetic or geometric progressions defined by recurrence relations, you can sum the terms using the arithmetic series and geometric formulae.
- To sum up the terms of other progressions, you may have to think about the series and find a clever trick.