5.2 Recurrence Relations

Sometimes it is extremely difficult to define a sequence by using a formula as above. Sometimes we can only define it by relating each term to the previous one(s).

This means we also require to know what the first term is so that we have something to start with. In these cases, U1 is the first term as before, but it is often easier to make U0 the term which you are actually given, and U1 then becomes the first term which you have actually calculated (i.e. the second term of the sequence).

I know that this seems complicated, but it can make life much simpler as you will see later on. At the end of the day, it doesn’t actually matter which way you do it, so long as you clearly state what your U0 and U1 are, and get the correct answer.

The name given to the type of formula which relates a particular term to whatever went before is recurrence relation.