In Maths, a number pattern is a set of numbers that follow a certain sequence or pattern. Number patterns can be of various kinds - you will find arithmetic patterns, geometric patterns and special patterns.

**Arithmetic number patterns**

In an arithmetic number pattern the difference between two consecutive terms remains constant. These patterns are usually created either by adding or subtracting a common number to create the sequence of numbers. The constant difference between two consecutive numbers in the pattern is also called the *Common Difference*.

For example: The sequence of even numbers is an arithmetic number pattern

2, 4, 6, 8, 10, 11, 12, 14, 16 …..

As is also the sequence of odd numbers

1, 3, 5, 7, 9, 11, 13, 15, 17, 19 ….

Here the common difference is 2.

Similarly, multiplication tables also represent arithmetic number patterns:

3, 6, 9, 12, 15, 18, 21, 24…

Here the common difference is 3. The number pattern continues by adding 3 to the last number.

**Geometric number patterns**

In a geometric number pattern the ratio between two consecutive terms remains constant. These patterns can be made by multiplying or dividing the same value each time. The value multiplied or divided each time is called the *Common Ratio*.

For example: 1, 3, 9, 27, 81, 243 …

In this pattern the common ratio is 3. You can continue the pattern by multiplying the last number by the number 3.

Similarly, the following sequence is obtained by dividing by 2

200, 100, 50, 25, 12.5 …

**Special number patterns**

There are some special number patterns such as square number sequence, cubic number sequences, Fibonacci number sequence.

In square number sequence the numbers are the squares of whole numbers.

0, 1, 4, 9, 16, 25, 36, 49, 64, 81 …

Similarly, the cube number sequence is made from the cubes of whole numbers.

0, 1, 8, 27, 64, 125 …

In the Fibonacci number sequence each number is the sum of the last two numbers in the sequence

0, 1, 1, 2, 3, 5, 8, 13, 21, 34

Here 1 is formed by adding (0 +1) = 1

The next number is found by adding (1 + 1) = 2

Similarly, (2 + 1) = 3

(3 + 2) = 5

And so on

**Number patterns worksheet**

Q1. Complete the following number pattern by identifying the common difference

3, 8, 13, 18, 23, 28, 33, 38, __, __

Answer:

There is a difference of 5 between each number. Hence, we can continue the pattern by adding the number 5 to the last number

3, 8, 13, 18, 23, 28, 33, 38, __43__, __48__

Q2. Complete the following number pattern by identifying the common difference

27, 25, 23, 21, 19, 17, 15, __, __

Answer:

The common difference is -2. The pattern can be continued by subtracting 2 every time.

27, 25, 23, 21, 19, 17, 15, __13__, __11__

Q3. Complete the following number pattern by identifying the common ratio

2, 4, 8, 16, 32, 64, 128, __, __

Answer:

There is a ratio of 2 between each number. Hence, we can continue the pattern by multiplying the last number by 2

2, 4, 8, 16, 32, 64, 128, 256, 512

Q4. Complete the following number pattern by identifying the common difference

87, 82, 77, 72, 67, 62, 57, __, __

Answer:

The common difference is - 5. The pattern can be continued by subtracting 5 every time.

87, 82, 77, 72, 67, 62, 57, 52, 47

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