Many people may not realize that house numbers, numbers on vehicle plates, etc. are examples of number patterns. Patterned numbers are part of mathematics, which can also be found in everyday life.

Another example is the game of billiards, where the balls are arranged in a triangle and form a pattern. If you look carefully, the arrangement of billiard balls has a pattern with the numbers 1, 2, 3, 4 and 5 balls from the top row to the bottom.

Examples of number patterns can also be found in biology lessons, specifically when amoeba reproduce by division. Each amoeba divides into two parts, then divides again, and so on.

## What is a number pattern?

From the many examples above, what are embossed numbers? Linguistically, pattern means permanent arrangement or form, while the definition of number is a quantitative unit symbolized by numbers.

Therefore, we can conclude that the definition of a number pattern is a quantitative unit symbolized by numbers that have a specific order. Patterned numbers can also be interpreted as a series of numbers accompanied by their own rules in an arrangement pattern.

## Types of number patterns and their formulas

Engraved numbers are divided into several different types, with each type having its own format. To make it more clear, look at the types of patterns with numbers and their respective formula below.

### 1. Strange engraved numbers

The first and most common type in everyday life are numbers with odd patterns. Odd patterns start from 1 to infinity, but the conditions must be odd, not even and so on.

- equation :
*Un=2n-1* - Example: 1, 2, 3,â€¦..11, 13, 15, 17, 19, 21 and so on.

In this formula “*n* ” is a series of numbers or natural numbers that you want to find.

### 2. Even engraved numbers

If there are odd-patterned numbers, there must also be even-patterned numbers. The pattern consists of even numbers that are divisible by 2 and start from the number 2 to infinity.

- equation :
*Un=2n* - Example: 2,4,6,â€¦.12,14,16,â€¦.,22,24,26, and so on.
- Note: n is a string of numbers

If you notice, for even numbers, all numbers displayed are divisible by 2.

### 3. Arithmetic patterns

Next, there are numbers with an arithmetic pattern, where the numbers that make them up always have a fixed difference between their terms. So, for example, the difference between the first and second order numbers is 3, then the difference between the second and third order numbers is also the same and so on.

- equation :
*un = a + (n-1)b* - Example: 4,8,12,16,20 and so on (difference 4)

The formula description is:

- a: The first term of the series of numbers in the pattern
- B: The difference in terms of numbers
- n: sequence of numbers

The formula of this arithmetic pattern is very useful in solving mathematical problems related to series of numbers.

### 4. Geometric pattern numbers

If the difference between two terms in a series of numbers has the same value in arithmetic-style numbers, this is completely different with geometric patterns. The definition of the pattern of geometric numbers is an arrangement of numbers such that the ratio between two terms is always a constant value.

- equation :
*un=RNA-1* - Example: 3,12,48, 192 and so on

From the formula and example above, the explanation is as follows:

- A: The first term in the order of numbers
- R: Racing
- n: sequence of numbers

For example, the numerical pattern above has a ratio of 4, where the second term is the first term multiplied by 4, the third term is the result of the second term multiplied by 4, and so on.

### 5. Square style

Square style numbers are numbers that have a pattern like a square and are made up of squares. It is said to consist of a square, because the number of rows on the side and top of the pattern is the same.

To clarify the matter further, you can see the square pattern in the numbers in the following image:

The formula for the pattern of square numbers is Un = n^{2}As shown in the picture. Examples of square numbers include 1, 4, 9, 16, 25, 36, 49, and so on.

### 6. Rectangular engraved numbers

The arrangement or pattern of numbers can also be formed into a rectangle. Although at first glance it doesn’t look much different from the square pattern, the formula for the two is actually different. Arranging the numbers in this pattern will form a flat rectangular shape.

What does a square pattern with numbers look like? See example below.

You can imagine that if you draw or place things in a rectangular arrangement, these are the numbers you will get. From the sample image above, we get examples of rectangular patterns for numbers, namely 2,6, 12, 20, and so on.

The formula for a number with a rectangular pattern is *One = n(n+1*).

### 7. Triangle pattern numbers

Another flat shape that can be arranged in a digital pattern is the triangle. An easy to find example is the arrangement of billiard balls. The illustration can be seen in the form below.

From the arrangement of the images above, we can get examples of numbers with a triangle pattern, namely 1, 3, 6, 10 and so on. The formula used in this pattern is *On = Â½ n (n+1).*

### 8. Fibonacci Pole

What is the Fibonacci pattern for numbers? A Fibonacci pattern is a number whose order starts from 0 and 1. The next digital segment is obtained from the sum of two consecutive segments.

Examples are 0.1,1 (0+1), 2 (1+1), 3 (1+2), 5 (2+3) and so on. So, the pattern starts with 0.1, then 1, which is the result of adding 0 and 1, then 1 plus 1 becomes 2, then 1 plus 2 equals 3, and so on.

The arrangement of numbers in a Fibonacci pattern can be seen in the following illustration.

The formula for the Fibonacci number pattern is Un = Un-_{1} + and_{-2}

### 9. Paula Pascal

There is still another type of pattern in numbers, which is Pascal. Understanding Pascal’s pattern in numbers cannot be separated from the triangular form. Pascal is the name of a physicist from France.

His discovery is known as Pascal’s triangle, which can also form a pattern in numbers. The Pascal style rules for numbers are as follows:

- The top row consists of one square, which is the number 1.
- The next rows in Pascal’s triangle must start with 1 and end with 1 as well.
- The number in the next square up to the second row is written to the infinite row (n), which is obtained by adding the two diagonal numbers above it.
- Every row in the triangle is symmetrical.
- The number of numbers in each row is a multiple of the number in the previous row.

If you are still confused, please take a look at the following illustration of Pascal’s triangle.

The formula used in Pascal style is Un = 2^{N-1}

## Examples of questions and discussion

There are several types of patterns in numbers and each has a different formula. Simply writing down theories and formulas is not enough if you cannot apply them to problems. To understand more about number patterns, look at the following example questions.

### 1. Example question 1

In a series of numbers, type 1, 5, 25, 125, 625,… What is the next number?

discussion :

First, pay attention to the difference between the two numerical terms in the model, which are 1 and 5 and 25 and 125 and 625, so you get the ratio x 5. So each subsequent numerical term is the result of the number in front of you multiplied by 5.

In the example you can see that 5 is the result of 1Ã—5, 25 is obtained from 5Ã—5, 125 is 25Ã—5 and so on. So the number in the next term is 625 x 5, which is 3125.

### 2. Example question 2

There is a number in the shape of a rectangle. What are the seventh and eighth numbers?

Discussion:

To find out how many digits are in the seventh and eighth positions in a rectangular number, first look at the formula. The formula for rectangular number patterns is Un=n(n+1).

Next, enter the numbers into the formula, if what you are looking for is the 7th and 8th order, then:

- U7 = 7 (7+1) = 7 x 8 = 56
- U8 = 8(8+1) = 8 x 9 = 72

From these calculations, the results show that the seventh and eighth positions in the rectangular model are 56 and 72.

### 3. Example question 3

A group of numbers that has an arithmetic pattern and starts from the number 5 and the difference between the two terms is 2. Write the sequence of numbers from the second order to the sixth order.

Discussion:

First find the formula for the pattern of arithmetic numbers, which is Un = a (n-1) b. Next, just enter the numbers into the formula, then:

- U2 = 5(2-1) x 2 = 5 x 2 = 10
- U3 = 5(3-1) x 2 = 5 x 4 = 20
- U4 = 5(4-1) x 2 = 5 x 6 = 30
- U5 = 5(5-1) x 2 = 5 x 8 = 40
- U6 = 5(6-1) x 2 = 5 x 10 = 50

So we get a series of arithmetic numbers in the order 5, 10, 20, 30, 40, 50.

### 4. Example question 4

For numbers with a triangular pattern, write the order from 2nd to 5th if the first term is 10.

Discussion:

First look at the formula for triangular numbers, which is Un = Â½ n (n+1). Then find the numbers in the order you want, which are:

- U1 = Â½ 1(1+1) = 1
- U2 = Â½ 2(2+1) = 3
- U3 = Â½ 3(3+1) = 6
- U4 = Â½ 4(4+1) = 10
- U5 = Â½ 5(5+1) = 15

From the calculations according to the formula, the following order is obtained 1, 3, 6, 10, 15.

Number patterns are numbers arranged according to a specific pattern. There are several types of engraved numbers and each arrangement has its own formula. These formulas are used to find numbers in a specific order.

Number patterns are not only found in mathematics subjects but are also applied in different things in life. Examples of number patterns that can be found in everyday life, such as house numbers, the arrangement of billiard balls, etc.