Sign In
A recursive rule, also known as recursive formula, defines each term of a sequence based on one or more of the preceding terms. Unlike explicit rules, recursive rules rely on previous terms to generate subsequent ones. An initial term must be provided to start the sequence. For example, consider the recursive rule for the Fibonacci sequence. F_n=F_(n-1)+F_(n-2) This rule states that each term in the Fibonacci sequence is the sum of the two preceding terms. Starting with the initial terms F_0=0 and F_1=1, subsequent terms are generated by adding the two previous terms together. The third term of the Fibonacci sequence will be found to illustrate this.
Another example of a recursive rule is for an arithmetic sequence. a_n=a_(n-1)+d In this formula, d represents the common difference.