Explicit Rule

An explicit rule, or explicit formula, of a sequence is a function rule where the input is the term's position index n and the output is the term's value a_n. This contrasts with recursive rules, as any term in the sequence can be found directly without needing knowledge of the previous ones. For example, consider the explicit rule for the sequence of even numbers. a_n=2n The 3^(rd) term of this sequence can be determined by directly substituting 3 for n into the formula. a_3=2*3 ⇒ a_3=6 Another example of an explicit rule is the Fibonacci sequence, whose explicit rule is the following. F_n=ϕ^n-(1-ϕ)^n/sqrt(5) In this rule, ϕ represents the golden ratio, which is approximately equal to 1.618.