# Patterns: Numbers

Number patterns are a series of numbers organized or repeated in some kind of order or into a design. The number patterns are additionally get described as a number sequence. In algebra, there are a lot of various kinds of sequences, like arithmetic and geometric sequences, etc.

Arithmetic Sequences are created via the addition or subtraction of the exact value every time. The value which is added or subtracted every time is known as the “common difference”

Geometric Sequences are created via multiplication of the same value every time. The element multiplied by every time is known as the “common ratio”.

Every day people see patterns of colors, actions, shapes, numbers, and more. In maths, sets of numbers get organized into a series, plus they’re related to one another based on a precise rule.

In these number patterns, the concept normally utilized is ordering. There are $$2$$ kinds of ordering: ascending and descending.

## Ascending Order

A series of numbers written in an order of lowest to the highest is called ascending order. For ascending order, the lowest number appears firstly and the biggest number at the end.

## Descending Order

A series of numbers written in an order of the highest to the lowest number is called descending order. In descending order, the highest number appears firstly, and the lowest number is at the end.

## Modes of Number Patterns

In most cases, there are $$3$$ kinds of modes for number patterns utilized in Maths: repeating, shrinking, and growing.

## Repeating Patterns

Repeating patterns are a string of numbers where the numbers or patterns repeat again and again. In the pattern shown here, several numbers or a group of numbers are shown repeating.
An Example:
$$1,\,2,\,3,\,4,\,5,\,1,\,2,\,3,\,4,\,5,\,1,\,2,\,3,\,4,\,5,\,….$$

## Growing Patterns

Growing patterns are a string of numbers where that get organized in growing order. For this sequence, the numbers are organized in ascending order.
An Example:
$$11,\,13,\,15,\,17,\,19,\,….$$

## Shrinking Patterns

A diminishing pattern is a series of numbers where these numbers are placed in a shrinking order. In this kind of series, numbers get placed in plunging order.
An Example:
$$15,\,13,\,11,\,9,\,…$$

The capability of recognizing number patterns is part of having a number sense, a talent we should practice to enhance our mathematical skills.

### Patterns: Numbers – Example 1:

Write the numbers that come next.

$$114,121,128,$$___,___,____

Solution:

Numbers are growing in the sequence, so our pattern is a growing pattern. By subtracting the first number from the second number we can find the common difference: $$121-114=7$$. Therefore, to find other numbers, we add $$7$$ to the obtained number each time: $$128+7=135, 135+7=142, 142+7=149$$. So, The answers to the question are$$135,142,149$$.

### Patterns: Numbers – Example 2:

Find missing numbers in the counting sequence.

___,___,$$52,47,$$___,$$37$$

Solution:

Numbers are shrinking in the sequence, so our pattern is a shrinking pattern. By subtracting the second number from the first number we can find the common difference: $$52-47=5$$. So, The answers to the question are$$62,57$$ and $$42$$.

## Exercises for Patterns: Numbers

Find two missing numbers in the counting sequence.

1. $$\color{blue}{8,16,32, , }$$
2. $$\color{blue}{422,411,400, , }$$
3. $$\color{blue}{ , ,82,94,106}$$
4. $$\color{blue}{235,250, , ,295}$$
1. $$\color{blue}{64,128}$$
2. $$\color{blue}{389,378}$$
3. $$\color{blue}{58,70}$$
4. $$\color{blue}{265,280}$$

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