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 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.

Related Topics

• Repeating Patterns
• Growing Patterns
• Even or Odd Numbers

Ascending Order

A series of numbers written in order from lowest to highest is called ascending order. For ascending order, the lowest number appears first and the largest number at the end.

Descending Order

A series of numbers written in order from the highest to the lowest is called descending order. In descending order, the highest number appears first, 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 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 descending 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 build 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 shrinking. 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})

How to find the rule of a number pattern

1. Find the differences. Subtract each number from the next one. If the difference is always the same, the rule is to add (or subtract) that amount. In 7, 12, 17, 22 the difference is always 5.
2. If the differences change, try dividing. Divide each number by the one before it. In 3, 6, 12, 24 each term is 2 times the last, so the rule is multiply by 2.
3. If neither works, look for a special pattern. Check whether the numbers are squares, odd numbers, or sums of earlier terms (see the table below).
4. Test your rule. Make sure it works for every pair of numbers, not just the first two, then use it to find the missing terms.

Special number patterns to know

Square and triangular numbers get their names from dot pictures: 9 dots fit in a 3 by 3 square, and 6 dots stack into a triangle with rows of 1, 2 and 3.

Frequently Asked Questions

What is a number pattern in maths?

A number pattern is a list of numbers that follows a rule, such as adding, subtracting, multiplying or repeating. In 7, 14, 21, 28, the rule is add 7, so the next number is 35. Patterns can go up (growing), go down (shrinking) or repeat a block of numbers like 1, 3, 1, 3.

What is a number pattern rule?

The rule is the instruction that takes you from one number to the next, such as “start at 2 and add 5” or “multiply by 3.” A rule can also give any term directly. For 5, 9, 13, 17, the rule add 4 also gives the formula 4n + 1, so the 10th term is 41.

How do you find patterns in numbers?

Compare neighboring numbers. First check the differences: if they are all the same, the pattern adds or subtracts that amount. If not, check whether each number is multiplied by the same value. In 3, 6, 12, 24, the differences change, but each number is doubled, so the next one is 48.

What is number patterns grade 2?

In 2nd grade, number patterns usually mean skip counting by 2s, 5s, 10s and 100s, and noticing what changes. For example, 15, 20, 25, 30 counts by 5s, and 340, 350, 360 counts by 10s, so only the tens digit changes. Students also say whether numbers in a pattern are odd or even.

What are number patterns and sequences?

A sequence is an ordered list of numbers, and a number pattern is the rule it follows. Arithmetic sequences add the same common difference each time, like 2, 8, 14, 20 (difference 6). Geometric sequences multiply by the same common ratio, like 2, 8, 32, 128 (ratio 4).

Is number patterns algebra?

Yes, number patterns are one of the first steps into algebra. When you describe a pattern with a rule, such as “the term is 3 times its position minus 1,” you are writing an expression: 3n − 1. That rule gives 2, 5, 8, 11 and lets you find the 50th term, 149, without listing them all.