Do you what number patterns are? Let us understand this with an example. 1, 4, 7, 10, 13, 16, … What numbers are these? These are the numbers following a certain pattern or sequence. Th number starts with 1 and jumps three numbers every time. Let us study some figures and number patterns in detail.

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## What does a Pattern Mean?

A pattern is a design or arrangement that repeats continuously. Let us identify the rule of the pattern of changing figures

Did you observe the pattern in the above figure? Observing the pattern we can find the rule for given pattern. The figures show the total of the numbers up to “n”.

- In the first figure, we can see that there are three dots. The 1st layer has = 1 + 2 = 3 dots
- In the second figure, we can see that there are six dots. The 2
^{nd}layer has = 1 + 2 + 3= 6 dots - The third figure shows six layers and has = 1 + 2 + 3 + 4 = 10 dots
- In the last figure, we can see four layers and the total numbers of dots are = 1 + 2 + 3 + 4 + 5 = 15 dots

## Patterns of Figures

Observe the figure given above. In the first figure, we can see that there are 4 triangles and 1 square. The second figure shows 6 triangles and 2 squares. In the third figure, we can see 8 triangles and 3 squares. The last figure has 10 triangles and 4 squares. Now can you guess the next figure?

Observing the above figures it is understood that the next figure will have 5 squares and 12 triangles. Let’s take one more example – identify the figure that will continue the series when the first and last figure is the same.

Can you answer this question? In this type of questions, a picture series will be given such that the first and last figures are the same. Now we need to find the figure from the given alternatives that will continue the series.

From the above figure, we can say that the first and last figures being the same, the figure to appear next will be the same as the second figure in the given question. Thus, the answer figure will be the same as the second figure.

## Number Patterns

Patterns can also be very commonly observed in numbers (series and sequences). Here are some square numbers follows a pattern:

1^{1 }= 1

11^{1} = 121

Further

111^{1} = 12321

1111^{1} = 1234321^{1
}Further

11111^{2} = 123454321

111111^{2} = 1234564321 and so on.

### Observe the Number Patterns

Find the next two term in the series 0, 5, 19, 15,…

Solution: We can see that in the series each of the previous numbers is added to 5 to get the new number hence the next numbers will be 15 + 5 = 20 and so 20 + 5 = 25

### Calender magic

Look at the calendar given below. Let us see some magic.

Can you find the total of these numbers in the box? Won’t it take some time? The total is 90. Did it take a long time to add these numbers? Let us see how you can add these numbers and get the answer even faster. Just take the middle number and multiply it by 9. *Addition of all the numbers in this square is = Middle number × 9 = 10 × 9 = 90*

## Solved Examples for You

**Question 1: Identify the rule which follows in the given figure series**

**Figure flips horizontally****It flips vertically****Figure rotates by 90° in a clockwise direction****Figure rotates by 90° in a counterclockwise direction**

**Answer :** D is the correct option. The arrow is rotating counterclockwise at every step. The relative position of the arrow and the 2 balls is the same.

**Question 2: Which number should be added to 32, so the resulting numbers read the same from left-to-right and right-to-left?**

**11****5****18****23**

**Answer :** D is the correct option. If we 32 from right, we get 23. So adding 32 to 23 gives 55. It reads same from left to right or right to left.

**Question 3: What is a pattern?**

**Answer:** It refers to a sequence or series that repeats. Moreover, mathematical sequences are a pattern that repeats as per a definite rule or rules. Besides, these rules are a definite way to calculate or solve a problem. We can observe a pattern in things like colors, shapes, actions, etc.

**Question 4: What is the recursive pattern rule?**

**Answer:** It is a pattern rule that tells you the start number of a pattern and how the pattern continues. For instance, a recursive rule for pattern 5, 8, 11, 14 … is start with 5 and adds 3. Here the explicit pattern rule uses the first time 5 and then each term has a common difference of 3.

**Question 5: Is there a pattern to random numbers?**

**Answer:** Some of the computer-generated random and non-random numbers aren’t actually random. Most importantly, they follow a subtle pattern that can be observed over a long period of time, or over many instances of generating random numbers.

**Question 6: How can we extend patterns?**

**Answer:** For extending the pattern, first of all, we have to understand the pattern of the sequence and the common difference between them. Once we are able to understand the pattern then we can extend the pattern to numbers we may like.

It is used to describe the pattern shown by the terms of a sequence