# Patterns

Mathematics is all about numbers. It involves the study of different patterns. There are different types of patterns, such as number patterns, image patterns, logic patterns, word patterns etc. Number patterns are very common in Mathematics. These are quite familiar to the students who study Maths frequently. Especially, number patterns are everywhere in Mathematics. Number patterns are all predictions. Few examples of numerical patterns are:

Even numbers pattern -: 2, 4, 6, 8, 10, 1, 14, 16, 18, …

Odd numbers pattern -: 3, 5, 7, 9, 11, 13, 15, 17, 19, …

Fibonacci numbers pattern -: 1, 1, 2, 3, 5, 8 ,13, 21, … and so on

## Patterns in Maths

In Mathematics, the patterns are related to any type of event or object. If the set of numbers are related to each other in a specific rule, then the rule or manner is called a pattern. Sometimes, patterns are also known as a sequence. Patterns are finite or infinite in numbers.

For example, in a sequence 2,4,6,8,?. each number is increasing by sequence 2. So, the last number will be 8 + 2 = 10.

## Number Patterns

A list of numbers that follow a certain sequence is known as patterns or number patterns. There are different types of number patterns:

- Arithmetic Pattern
- Geometric Pattern
- Fibonacci Pattern

## Rules for Patterns in Maths

To construct a pattern, we have to know about some rules. To know about the rule for any pattern, we have to understand the nature of the sequence and the difference between the two successive terms.

**Finding Missing Term: **Consider a pattern 1, 4, 9, 16, 25, ?. In this pattern, it is clear that every number is the square of their position number. The missing term takes place at n = 6. So, if the missing is x_{n, }then x_{n} = n^{2}. Here, n = 6, then x_{n} = (6)^{2} = 36.

**Difference Rule:** Sometimes, it is easy to find the difference between two successive terms. For example, consider 1, 5, 9, 13,……. In this type of pattern, first, we have to find the difference between two pairs of the sequence. After that, find the remaining elements of the pattern. In the given problem, the difference between the terms is 4, i.e.if we add 4 and 1, we get 5, and if we add 4 and 5, we get 9 and so on.

### Types of Patterns

In Discrete Mathematics, we have three types of patterns as follows:

**Repeating**– If the number pattern changes in the same value each time, then the pattern is called a repeating pattern. Example: 1, 2, 3, 4, 5, ……**Growing**– If the numbers are present in the increasing form, then the pattern is known as a growing pattern. Example 34, 40, 46, 52, …..**Shirking**– In the shirking pattern, the numbers are in decreasing form. Example: 42, 40, 38, 36 …..

### Solved Example

**Example 1: **

Determine the value of P and Q in the following pattern.

85, 79, 73, 67, 61, 55, 49, 43, **P, **31, 25, **Q.**

**Solution:**

Given sequence:85, 79, 73, 67, 61, 55, 49, 43, **P, **31, 25, **Q.**

Here, the number is decreasing by 6

The previous number of P is 43. So, A will be 43 – 6, P = 37

The previous number of Q is 25. So, B will be 25 – 6, Q = 19

Therefore, the value of P is 37 and Q is 19.

**Example 2: **

Determine the value of A and B in the following pattern.

15, 22, 29, 36, 43, **A, **57, 64, 71, 78, 85, **B.**

**Solution:**

Given sequence: 15, 22, 29, 36, 43, **A, **57, 64, 71, 78, 85, **B.**

Here, the number is increasing by +7

The previous number of A is 43. So, A will be 43 + 7, A = 50

The previous number of B is 85. So, B will be 85 + 7, B = 92

Therefore, the value of A is 50 and B is 92.