In mathematics, whole numbers are natural numbers, including zero. Number pattern means a representation of a number so that it can be understood by everyone quickly. In addition, it builds a typical relationship between whole numbers. Number patterns are not restricted to one type. They can be of any order – ascending, descending, cube, square, multiples, even, odd, etc.
Everyone uses them because of their various designs, sequences and patterns. They are easy to understand by everyone, even by those who do not understand numbers. If one solves mathematical problems using patterns, then their mathematical reasoning and logical thinking increase.
Here is the list of some commonly used number patterns in mathematics
1. Ascending order – In this, the numbers are arranged from smallest to biggest. This pattern is the most commonly used one to represent number patterns. For example, 2, 6, 9, 15, etc.
2. Descending order – In this, the numbers are placed from largest to smallest. It is opposite to the ascending order of the number pattern. For example, 100, 97, 78, 65, 43, etc.
3. Even numbers – The numbers which are multiples of 2 are known as even numbers. The number pattern can be of difference 2, or any other even number; still, the sequence will be even. For example, 6, 12, 18, 24, etc.
4. Odd numbers – They are represented by the formula 2n1, where n is the set of natural numbers. The number pattern may contain a normal odd number sequence or numbers in the sequence of other odd numbers like 5, 7, 9, etc. For example, 7, 21, 35, 49, etc.
5. Square numbers – The number pattern can be made with square numbers. For example, 2, 9, 16, 25, etc.
6. Cube numbers – The number pattern can be made with cubes of numbers, like 8, 27, 64, etc.
7. Arithmetic sequence – The number pattern whose difference is the same along the series is known as an arithmetic sequence. For example, 500, 1000, 1500, etc.
8. Geometric sequence – The number pattern whose ratios are the same is known as a geometric sequence. For example, 420, 490, 560, etc.
9. Fibonacci numbers – The pattern made with numbers upon successive addition is known as a Fibonacci sequence. For example, 2, 2, 4, 6, 10, etc.
The most commonly used pattern to represent numbers is the dot pattern. Different arrangements of dots represent numbers, like rectangular patterns, squares, triangles, lines, etc. Thus, every whole number can be represented by the dot pattern.
Line pattern – In this, a pattern is made in a simple array of dots representing the numbers.
Square pattern – This can be done when the numbers are even and arranged equally in rows and columns.
Rectangular pattern – This can be used to make a pattern with any numbers. However, if the numbers are left asymmetrically, then a triangle pattern may form.
Triangle pattern – A Triangle pattern denotes unequal numbers that cannot be placed in rows and columns correctly.
Numbers  Line representation  Square representation  Rectangle representation  Triangle representation 
2  ●●  
5  ●●●  ●● ● 

4  ●●●●  ●● ●● 

6  ●●●●●●  ●● ●● ●● 

7  ●●●●●●●  
10  ●●●●●●●●●●  ●●●●● ●●●●● 
●●●● ●●● ●● ● 

13  ●●●●●●●●●●●●● 