Difference Between Pattern and Sequence

Pattern vs Sequence

It is difficult to give an exact definition for the term “Pattern”. More generally, it means repetition of event or objects in a particular manner. Study of patterns is used in many fields such as mathematics, bio science and computer science. The definition or use of term ‘pattern’ may differ from field to field. We can find patterns in many areas of mathematics such as arithmetic, geometry, logic and so on. Recurring decimals are one example. A recurring decimal consists of a sequence of digits, which repeat infinitely. For an example, 1/27 equals to the recurring decimal 0.037037… the sequence of numbers 0, 3, 7 will repeat forever. However, not all patterns involve repetition.

Sequence on the other hand, is a clearly defined mathematical term. A sequence is a list of terms (or numbers) arranged in a definite order. A sequence contains members, which are sometimes called elements or terms, and the number of elements is called the length of the sequence. There are finite and infinite sequences. There is no restriction on terms in the sequence.

The example ( A, B, C, D) is a sequence of letters. This sequence differs from the sequence (A, C, B, D) or (D, C, B, A), as the order of elements are different.

Some sequences are simply random values, while some sequences have a definite pattern. However, a sequence should follow some rules for calculating on it. Arithmetic and geometric sequences are two such sequences with a definite pattern. Sometimes, sequences are called arithmetic functions. Most commonly, n^th term of a sequence is written as a_n. For an example, 5, 7, 9, 11 … is an arithmetic sequence with a common difference of 2. The n^th term of this sequence can be written as a_n = 2n+3.

For another example, let us consider the sequence 2, 4, 8, 16… This is a geometric sequence with a common ratio 2. The n^th term of the geometric sequence is a_n = 2ⁿ.