- Written By Srotaswini Mohapatra
- Last Modified 21-10-2022
Types of Patterns:Types of patterns is a fundamental concept that will help students understand different chapters in Mathematics. We can observe patterns in our daily lives, including colours, shapes, actions, sounds or other sequences that repeat everywhere. The sequence in which things are arranged is referred to as a pattern. Once students have adequate knowledge of patterns, they will be able to identify them all around them.
Students usually look for all type of chart patterns, types of candlestick patterns, types of curl patterns, etc. We need to understand the elements within the pattern unit and how it repeats. If we see only XY, we do not have enough evidence to identify the pattern. However, we can be confident in our judgment if we see XY repeating, such as XYXYXY. Read this article to learn more about types of patterns.
Types of Patterns: Which Type of Design Patterns Concern Class and Object Composition
Patterns include a series orsequencethat repeats itself. The elements of a pattern repeat in a predictable manner. The patterns that we observe in our daily lives are those of colours, actions, words, letters, numbers, etc.
They can be related to any event or object and can be finite or infinite. In Mathematics, patterns are a set of numbers arranged in a sequence such that they are related to each other in a specific rule. The rules define a way to calculate or solve problems.
For example, in a sequence of \(2,4,6,8,10,…..,\) each number is increasing by \(2.\) So, according to the pattern, the next number will be \(10 + 2 = 12.\)
Patterns: Types
There are three types of patterns.
- Letter Pattern
- Number Pattern
- Shape Pattern
Let’s see each pattern in detail.
Letter Pattern
A letter pattern is a pattern or sequence in a series of letters or English alphabets. This pattern generally establishes a common relationship between all the letters.
Example: A, D, G, J, M, P.
By observing the above pattern, it is very clear that the consecutive two letters are missing if we go by the universal sequence of \(26\) letters of English Alphabet.
Number Pattern in Maths
Number Patternis apattern in a series ofnumbers. Thispatternnormally establishes a common relationship between allnumbers. Let us discuss some types of patterns in Maths:
Arithmetic Pattern
An Arithmetic Pattern is also known as the Algebraic Pattern. It is a sequence of numbers based on addition or subtraction to form a series of numbers related to each other. If two or more numbers in the sequence are given, we can use addition or subtraction to find the arithmetic pattern. We can also determine the missing number in a given sequence by using addition or subtraction.
Geometric Pattern
The geometric pattern is a sequence of numbers that are based on multiplication and division. If two or more numbers in the sequence are provided, we can easily find the unknown numbers in the pattern using multiplication and division operations.
Example: \(3,9,27,81,243,729.\)
From the above pattern, it can be seen that each number is obtained by multiplying \(3\) with the previous number.
Fibonacci Pattern
The Fibonacci Pattern is a sequence of numbers in which each number in the sequence is obtained by adding the two previous numbers together. The sequence starts with \(0\) and \(1.\)
Example: \(0,1,1,2,3,5,8,13.\)
Here, we can see: \(0 + 1 = 1,1 + 1 = 2,1 + 2 = 3,2 + 3 = 5,3 + 5 = 8.\)
Triangular Number Pattern
The triangular number sequence is the representation of the numbers in the form of an equilateral triangle arranged in a series or sequence. These numbers are in a sequence of \(1,3,6,10,15,21,28,36,45,\) and so on. The numbers in the triangular pattern are represented by dots.
Example:
By observing the above pattern, we get,
Picture 1: There is only \(1\) small circle. That means \(0\) (the number of shape in the previous shape) \(+1.\)
Picture 2: There are \(3\) small circles. That means \(1\) (the number of shape in the previous shape) \(+2.\)
Picture 3: There are \(6\) small circles. That means \(3\) (the number of shape in the previous shape) \(+3\)
Picture 4: There are \(10\) small circles. That means \(6\) (the number of shape in the previous shape) \(+4\)
Square Number Pattern
In the square number pattern, each consecutivesquare numberis the result of adding the next consecutive oddnumber.
Example: \(1,4,9,16,25,….\)
\(1\) is the square of the number \(1.\)
\(1 + 3,\) here, the square number is \(4.\)
\(1 + 3 + 5,\) the next square number is \(9\) and so on.
Cube Number Pattern
In a cube number pattern, the number sequences are sets of numbers that follow a pattern or a rule. It is the cube of numbers.
Example: \(1,8,27,64,125.\)
Shape Pattern
Shape patternsoccur when a group ofshapesare repeated. Thesepatternsfollow a certain sequence or order ofshapes,i.e., they are repeated at least two times. Theshapescan be simpleshapeslike circles, squares, rectangles, triangles or other objects such as arrows, flowers, moons, and stars.
Example:
The above shape pattern consists of a circle, triangle, pentagon, and star. Again it repeats in the same sequence or order.
Type of Candlestick Patterns
Candlestick patterns are created by grouping two or more candlesticks in a certain manner.They are used by technical analysts to identify trading patterns and set up trades.Candlestick chartshave their origin in Japan.This was there 100 yearsbeforethe bar charts and point-and-figure chartswere there in use.The white rectangular partof the candleis called the “real body”.It shows the link betweenthe opening and closing prices. Candlestick patterns can be classified into:
- Continuation Patterns
- Bullish Reversal Patterns
- Bearish Reversal Patterns
Type of Chart Patterns
Another kind of pattern used for technical analysis is the chart pattern.A chart pattern is a shape within a price chart that helps topredict the activitiesof priceslooking at pasttrends.Chart patterns fall under three broad categories:
- Continuation patterns –these patternssignify the continuation of an ongoing trend.
- Reversal Chart pattern –these patterns indicatea change in direction to a trend.
- Bilateral chart pattern –these battles indicatehigh volatilityof markets
Examples of Patterns in Math
Let us discuss some examples of patterns used in math:
Example 1: An arithmetic decreasing pattern is given below.
Example 2: An arithmetic increasing or progressive pattern is given below.
Example 3: Triangle pattern consists of dots are given below.
Types of Patterns: Rules
Students also look for all types of chart patterns. To create a complete pattern, there are a set of rules to be considered. To applythe rule, we need to understandthe nature of the sequence and the difference between the two successive numbers.It takes some amount of guesswork and checking to see whether the rule works throughout the whole series.
There are two basic divisions to find out the rules in number patterns:
- When the numbers in the given pattern get larger, they are said to be in ascending order. These patterns normally involve addition or multiplication.
- When the numbers in the given pattern get smaller, they are said to be in descending order. These patterns normally involve subtraction or division.
Types of Patterns: Notes
Let us remember some notes on different patterns,
- The number patterns could be ascending, descending, multiples of a certain number, or series of even numbers, odd numbers, etc.
- Learning patterns enhances our capability to observe patterns. Observing a pattern pushes us to think and identify the rule which can continue the pattern.
- Patterns can be of shapes, objects, and colours as well and not just numbers.
- In an arithmetic sequence, each successive term is obtained by adding the common difference to its preceding term.
- In a geometric sequence, each successive term is obtained by multiplying the common ratio to its preceding term.
Solved Examples – Type of Patterns
Let us look at some of the solved examples:
Q.1: Find the rule for the below pattern.
Ans: Rules are a way to solve mathematical problems.
By observing the above-given pattern we get,
Picture \(1:3 \times 1 + 2\)
Picture \(2:3 \times 2 + 2\)
Picture \(3:3 \times 3 + 2\)
Picture \(4:3 \times 4 + 2\)
Hence, the rule for the given pattern is shown above.
Q.2. Give one example of a number pattern.
Ans: One example of a number pattern is \(1,3,5,7,9,11,13,15.\) This pattern consists of all the odd numbers. So, it is called a pattern of odd numbers.
Q.3. Fill in the missing shape to complete the below pattern.
Ans: By observing the above pattern, we get, there is a repetition of diamond, star, triangle, triangle. So, the missing shape must be a star.
Hence, the complete pattern is given above.
Q.4. Determine the value of \(C\) and \(D\) in the below pattern.
\(22,29,36,43,C,57,64,71,78,85,D,99\)
Ans: The given pattern: \(22,29,36,43,C,57,64,71,78,85,D,99\)
Here, the number is increasing by \( + 7\)
The previous number of \(C\) is \(43.\) So, \(C\) will be \(43 + 7 = 50.\)
The previous number of \(D\) is \(85.\) So, \(D\) will be \(85 + 7 = 92.\)
Hence, the value of \(C\) is \(50,\) and \(D\) is \(92.\)
Q.5. Identify the type of pattern for the sequence \(8,12,16,20,24,28.\)
Ans: Pattern \(8,12,16,20,24,28\) is an arithmetic pattern, as each term in the pattern is obtained by adding \(4\) to the previous term.
Patterns: Summary
In this article, we covered the definition of pattern, its types with definition and examples, some rule to find the types of pattern, notes etc. We solved some examples on how to complete a pattern and how to identify the type of pattern etc. It will help the student to know the detail of the patterns.
FAQs on Type of Patterns
Frequently asked questions related to types of patterns is listed as follows:
Q.1: What are examples of patterns?
Ans: Patterns include a series or sequence that generally repeats itself with certain rule or rules.
Some examples of number patterns are:
Example 1: \(1,4,9,16,25,36,49\) (pattern consists of the square of numbers from \(1\) to \(7\)).
Example 2: \(0,2,4,6,8,10\) (Pattern of the even numbers)
Q.2: What are the two types of pattern in math?
Ans: The two types of patterns in math are number pattern and shape pattern.
Q.3: What are the different types of patterns in math?
Ans: There are three types of patterns in math. These are number patterns, letter patterns and shape or geometric patterns.
Q.4: What is called a shape pattern in math?
Ans: When a sequence ofshapesis repeated more than two times, it forms a shape pattern. To find ashape pattern, we need to identify the sequence ofshapesthat is being repeated and to complete ashape pattern, we need to look at the lastknown shapeand then add the nextshapein the sequence.
Q.5: What are the 4 types of sequence in math?
Ans: There are \(4\) types of sequence in math. Theses are given below:
- Arithmetic Sequences
- Geometric Sequences
- Harmonic Sequences
- Fibonacci Numbers
