Math Patterns

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A Pattern defines a group of numbers in which all the numbers are related with each by a specific rule. A pattern is the process of multiplying the preceding term by a constant factor. Such a sequence is called patterns. Patterns give us immense joy to find the relationship between the numbers which different number forms patterns. The constant factor is called common ratio (C.R) in patterns. We are going to explain pattern called numerical patterns.

Types of Patterns:

Below are the types of patters:

• Arithmetic Pattern.
• Geometric Pattern.

Arithmetic Pattern: Let the term a₁ is used to denote the first term, a₂ for the second term . . . and for the nth term we can use a_n and d represents the common difference between the terms. This value is equal. Then the AP becomes a₁, a₂, a_3, . . a_n. So, a₂ – a₁ = a₃ – a₂ = . . . = a_n – a_{n – 1} = d.

Then the common form of the arithmetic sequence is a, a + d, a + 2d, a + 3d, …….

An Example of Arithmetic Progression is 6, 9, 12, 15………

The n^th term of the A.P is find by the formula t_n = ar^n-1

Geometric Pattern: A geometric progression pattern is the list of terms as in an arithmetic progression but in this case the ratio of successive terms is a fixed value.

An example of a geometric progression pattern is

2,8, 32,128 ……………

r is used to denote the ratio of successive terms and a is the first term of the sequence.

The n^th term is given by t_n = ar^n-1

Here a is the first term and r is the common ratio.