New Notations A recursive formula expresses each new term of a sequence based on the preceding term in the sequence. The recursive formulas to determine the nth term of an arithmetic sequence and a geometric sequence are shown. Arithmetic Sequence common difference nth term Geometric Sequence common ratio nth term an 5 an 2 1 1 d gn 5 gn 2 1 ? r previous term previous term The explicit formula represents the sequence as a function. The explicit formulas to determine the nth term of an algebraic sequence and a geometric sequence are shown. Arithmetic Sequence common difference © Carnegie Learning, Inc. nth term an 5 a1 1 d(n 2 1) 1st term previous term number Geometric Sequence nth term previous term number gn 5 g1 ? r n 2 1 1st term common ratio TOPIC 2: Sequences • M1-79E