Short Note On The Number Series

Numbers, numbers, words, and letters are all part of a series. It is a sequence if it follows a specific pattern. Students must decipher a set of established rules hidden inside the questions in order to arrive at the correct answer.

For example, consider 1, 4, 7, 10, 13… Here, the difference between consecutive numbers is 3. It’s worth noting that, with the exception of the very first number, every other number in the sequence has some sort of rule relating it to the number before it.

What are the types of number series?

• Arithmetic series: In this type, the series is continued by adding or subtracting a certain number. The differences between the numbers are consistent throughout the series.

For example: 5, 10, 17, 26, 37, 50, 65

In this number series, there is a pattern 

5         10            17           26             37               50                    65

    +5          +7            +9           +11            +13                 +15

            +2           +2           +2              +2                +2

• Geometric series: In this type, the series is continued by multiplying or dividing by a certain number. Here, the ratio between consecutive terms is large, increases in a particular way, and is constant throughout the series.

For example: 4, 12, 36, 108, 324, 972

4          12            36            108                324                  972

     ×3          ×3             ×3                ×3                   ×3

• Arithmetic-geometric series: As the name implies, this series is a combination of arithmetic series and geometric progression. An important characteristic of such a series is that the differences between consecutive terms are in geometric progressions.
• Product series: In this type of series, each term is multiplied by a fixed number or a pattern of numbers to get the next consecutive number.
• Difference series: The difference series can be further classified as a series of constant difference numbers; there is always a constant difference between two consecutive numbers. In a sequence where the difference increases or decreases, the difference between two consecutive numbers increases or decreases. In a series of numbers where the difference increases or decreases, the difference between two consecutive numbers decreases.
• Division series: In this type of series, each term is divided by a fixed number or a pattern of numbers to get the next consecutive number.
• Square or cube series: This type of sequence of numbers progresses as the number is squared or cubed.
• Mixed series: This type contains multiple row patterns. In general, these types of questions are a bit complicated.

What are the patterns in number series?

A number pattern is usually a sequence or pattern of a set of terms. For example, the number pattern on the next line is +5. 

0, 5, 10, 15, 20, 25, 30 ……… 

To solve the number pattern problem, check the pattern rules carefully. 

Try adding, subtracting, multiplying, or dividing between consecutive terms.

Conclusion: 

In summary, when dealing with problems with number series and patterns, we need to look at the relationship between these numbers. You need to look for arithmetic relationships such as subtraction and addition. Divide and multiply the terms to find the geometric relationships and find their common ratio.