How to Solve Number Series Related Questions?

In this article, we will be learning to solve a number of related problems both theoretically and practically with help of some examples and practice problems. Two adjacent numbers in the sequence are related by an identical relation. A number series can comprise positive or negative numbers.

What is a number series?

A number series consists of numbers following a particular rule or system of arrangement. Here, any two adjacent numbers in the sequence are related by an identical relation. Thus, any number missing out from the series can be obtained by performing mathematical operations in either the previous or the following number of the missing number. The numbers of a number sequence are generally related by addition, subtraction, multiplication, or division. There can be different number series containing numbers like natural numbers, integers, whole numbers, and rational numbers. Number series can also consist of only positive or negative numbers. Many other kinds of number series are used and asked in various examinations.

Tips and tricks to solve number series questions

Now that we know what number series is, let us learn some tips and tricks to decode these number series questions.

These questions are generally asked in the logical reasoning section of different competitive exams.

The main step is to identify the relation between the given numbers to solve these questions. 

For instance, the following number of the sequence can be found easily from the prevailing relations. 

To identify the relation, check the given numbers and put different operations on them by the hit and trial method.

Moreover, we can identify the arithmetic operator through a few conventional tricks as given below:

1. If the number series gradually decreases, then the arithmetic operation is subtraction.
2. If the number series is gradually increasing, then the arithmetic operation is addition.
3. If the ratio between any two consecutive numbers on the sequence is identical, the line is a Geometric Progression (GP) series.
4. If the difference between any two consecutive numbers on the sequence is the same, then the sequence is an Arithmetic Progression (AP) series.
5. Have a strong knowledge of the cubes and squares of different numbers so you can recognise the pattern at once.
6. If there is no direct relation between two consecutive numbers, but there is a relation between alternate numbers, then the series is a hybrid of two sequences. Solve the two sequences separately to obtain the result.
7. If the sequence numbers are increasing in a multiplicative manner, then the arithmetic operator used is multiplication.

Sample questions for the number series

There are two types of questions asked from number series:

1. To find out the missing or following sequence number.
2. To point out the wrong number amongst the sequence.

Following the above steps we can find out the relation. Solving type 1 questions becomes absolutely easy.

To solve type 2 questions, we will find the relation used in the sequence and check whether every number satisfies the relation. Any number that violates the sequence is the wrong one.

Let us see an example of number series questions.

1. Find out the missing number in the series,

                4, 16, 36,…, 100

Ans: In this series, using our pre-requisite knowledge, the squares of 2, 4, 6,  and 10 are given. Thus, this is a sequence of squares of even numbers. 

Therefore, the missing number is a square of 8, which is 64.

The final sequence is: 4, 16, 36, 64, 100.

Solved examples of number series questions

1. Find out the next number on the sequence 12,7,2,….

Ans: As this series is gradually decreasing, it is a subtraction series with a difference of 5 between two numbers.

Therefore, next number = 2-5

                                        =-3

So, the final sequence is 12,7,2,-3.

2. Find the missing number from the sequence 3,9,27,…,243.

Ans: On close observation, we find that this series is a sequence of 3^1,3^2,3^3… and so on.

Therefore, the missing number is 3^4 = 81.

So, the final sequence is 3, 9, 27, 81, 243.

3. Find out the missing number from the sequences 2,7,17,…,52.

Ans: As this series is gradually increasing, it is an additional series with a difference of 5 between the two numbers. With each succession, the addition also increases by 5.

Therefore,

2 + 5 = 7; 7 + 10 = 17; 17 + 15 = 32; 32 + 20 = 52.

Therefore, the missing number of the sequence is 32.

Final sequence = 2, 7, 17, 32, 52.

Conclusion

In this article, we have learned about the ‘number series’. We have observed what a number series is and the possible types. The article describes various tips and tricks to solve questions on number series. The types of questions are asked from number series and seen as a sample question of number series. To get a better clarification of our knowledge, we have seen several solved examples in this domain. I hope the readers are satisfied with the knowledge gained through this article.