There are two sorts of formulas that can be used to calculate a particular
term of a series.

One is an explicit formula requiring only that you know the ordinal number of
the term you want to calculate.  Example,  is the nth odd number, so
you can say that the 11th odd number is 

The other type is the recursive formula that requires you to know the
term previous to the one you wish to calculate, but that, in turn 
requires you to know the term previous to that, etc., all the way 
back to the beginning.  An example is the Fibonacci Sequence where the first
two terms are 1 and each succeeding term is the sum of the previous two,
1, 1, 2, 3, 5, 8...


The actually is no "the" recursive formula.  Rather, there are as many 
recursive formulas as there are sequences that require that sort of a
descriptor -- in other words, there is an infinity of them.