An explicit rule of a sequence is a function rule where the input is a term's position, and the output is the value of the term. This is opposed to recursive rules, where a term's value is found using previous terms. Explicit rules are often written as
an=f(n),
where f(n) is the function rule. An example would be the sequence 2,3,4,…, which can be described by the explicit rule
an=n+1,
where n is the position of a term in the sequence. It says that the first term, a1, has the value 2, the second term, a2, has the value 3, and so on.