Patterns in mathematics may be either numerical or visual. Three common numerical patterns (also referred to as sequences) are arithmetic, geometric, and exponential.

Common Numerical Sequences

In an arithmetic sequence, a common difference exists between a term and its previous term. For example, the sequence {1, 2, 3, 4, 5} has a difference of 1 between every term, making it arithmetic.

Geometric sequences have a common ratio, that is, a multiplying number, between every term. For example, the sequence {3, -6, 12, -24} is geometric because it has a common ratio of -2.

Finally, an exponential sequence has a base, or a number, that is raised by an increasing power. For instance, the sequence {1, 2, 4, 8, 16} = {2⁰, 2¹, 2², 2³, 2⁴} is exponential with 2 as the base.

Visual Sequences

Visual sequences may consist of geometric objects, a form often used in standardized tests. Usually, the sequences can be equated to a numeric pattern. For example, the number of sides in each figure can...