Number Patterns

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Introduction to Number Patterns

In mathematics, the number pattern is a pattern or sequence in a number series. A common relationship between all numbers is generally formed by this pattern.

Ex: 1, 3, 5, 7, 9, 11, 13, ........ these number patterns represent the sequence of odd numbers.


Types of Number Patterns

There are two common number sequence patterns:

  • Arithmetic Sequences

  • Geometric Sequences

The special sequences of number patterns are as follows:

  • Square Numbers

  • Cubic Sequence

  • Triangular Numbers

  • Fibonacci Numbers

Arithmetic Sequence

In Mathematics, the Arithmetic sequence is a sequence of numbers in which the difference between consecutive terms is constant. This difference between consecutive terms is called a common difference.


For example, consider the following arithmetic number series: 

1, 4, 7, 10, 13, 16, ...... is an arithmetic sequence because the difference between consecutive terms is 3.

1, 4, 8, 11, 15, 18, ...... is not an arithmetic sequence because the difference between consecutive terms is not a constant.


Geometric Sequences

A geometric progression is a sequence of non-zero numbers, where each term after the first is found by multiplying the previous one with a fixed, non-zero number called the common ratio.


For example:

4, 8, 16, 32, 64, ...... is a Geometric sequence because the step is multiplied by 2 which is the common ratio.

4, 8, 12, 16, 20, 24, ...... is not a Geometric sequence because the common ratio between each step is different.


Square Numbers

In Mathematics, an integer that is the square of an integer is a square number. For example, 16 is a square number which is a square of the number 4. Denoted by 42 or 4*4.

The square number patterns for the first 10 numbers will be as follows:

1, 4, 9, 16, 25, 36, 49, 64, 81, 100.

Here we observe the square number pattern the first number in the pattern is a square of 1 followed by a square of 2 which is 4, a square of 3 is 9 and so on till the square of 10 is 100.


Cube Numbers

A number that is 3 times multiplied by itself is a cube number. For example, 27 is a cube number which is a cube root of 3. Denoted by 33 or 3 * 3 * 3.

The Cubic Sequence for the natural numbers will be as follows:

1, 8, 27, 64, 125, 216, 343, 512, ............


Triangular Numbers

Objects arranged in an equilateral triangle are counted by a triangular number. In a triangular arrangement with n points on one side, the nth triangular number is the number of dots and is equal to the sum of the n natural numbers from 1 to n.

The number of the pattern of dots that form a triangle will give a triangular number sequence which is as follows:

1, 3, 6, 10, 15, 21, 28, 36, …


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Fibonacci Numbers

Fibonacci Numbers are a sequence of numbers such that each number is the sum of the two preceding ones, starting from 0 and 1.

The Fibonacci sequence is as follows:

0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, ……..

Here the third number in the sequence is 1 which is the sum of 1 + 0. Similarly, the 6th number is 5 which is the sum of the 4th and 6th number 2 + 3.


Questions on Number Sequence Examples

Question: Arrange the given list of numbers based on the different sequences.

  1. 10, 15, 20, 25, 30, 35, ……..

  2. 100, 121, 144, 169, 225, ………….

  3. 9, 27, 81, 243, 729, …………….

  4. 125, 216, 343, 512, ………….

Answer: 

  1. The given sequence is an Arithmetic sequence because the common difference between the consecutive terms in the sequence is 5.

  2. The sequence is a square number pattern where 100 is a square of 10, 121 is a square of 11, and so on.

  3. The sequence is a Geometric sequence because the common ratio between the consecutive terms is 3. 

  4. The given sequence is a Cubic Sequence where the number.

Question: Find the missing number in the given sequences and name the type of sequence.

  1. 10, 17, 24, _, 38, 45.

  2. 16, _, 36, 49, 64.

  3. 16, 32, 64, _, 256, 512.

Answer: 

  1. The missing number is 31. Because this is an arithmetic sequence with a common difference between the consecutive terms as 7.

  2. Here the missing number is 25. This is a square number pattern that starts from squaring the number 4 which is 16 and 5 is 25, 6 is 36, 7 is 49, and 8 is 64.

  3. Here the missing number is 128. This is a Geometric sequence because the common ratio between the consecutive terms is 2.

FAQ (Frequently Asked Questions)

1. What is the Number Pattern?

Ans: The number patterns are the pattern in which a number of lists follow a certain sequence. The patterns usually determine the relationship between two numbers. It is also known as the sequences of series in numbers.

2. What are Common Types of Number Patterns?

Ans: There are two common types of number patterns:

  • Arithmetic Sequences

  • Geometric Sequences

3. What are the Special Sequences of Number Patterns?

Ans: There are four special sequences of number patterns:

  • Square Numbers

  • Cubic Sequence

  • Triangular Numbers

  • Fibonacci Numbers