Missing Numbers

Mathematics involves questions of problem-solving for the students. Problems of Missing numbers are important for all the students. Logical and problem-solving questions like Missing numbers are part of a variety of entrance exams and competitive exams of Management, Architecture, Business, Administration, Civil Services exams and Engineering exams etc. 

In this article of Vedantu, students can learn the definition of Missing numbers, Missing number series, Steps to find Missing numbers in the Series, quiz to find missing numbers, Missing numbers in a sequence and Solved examples to find Missing numbers in Sequence.

What are the Missing Numbers?

Missing numbers are the numbers that have been missed in the given series of a number with similar differences among them. The method of writing the missing numbers is stated as finding similar changes between those numbers and filling the missing terms in the specific series and places. In this article we will learn what are missing numbers, missing number series, how to find missing numbers in the series and sequence with examples, solved examples on missing numbers in the series and sequence, etc. 

Missing Number Series

We have seen that number series is a collection of numbers that follows a particular rule or formula. There are various types of series and missing number series is one among them. In missing number series, a series is given with one missing number and you are asked to find the missing term. To find the missing number, we first identify the rule or formula which is applied in the given missing number series. Let us learn the method to find the missing number in a series.

How to Find The Missing Number in A Series?

In the given missing number series, you can sometimes find missing numbers at the beginning or at the end of the series. The layout in the missing number series is similar to the wrong number series, you have to identify the rule and then use the rule to estimate the next number.

Here Are The Steps To Find The Missing Numbers In A Series

1. Select 2 or 3 terms to the text which rule will be applied to find the missing number. For example: If you have 5 numbers in a series then pick the first 3 terms to check the rule that is to be applied.

2. While choosing the number to check the rule, select the number that is easy to operate. These include terms that are factors of 2, 3, 5, or 10. Check the series with some common methods such as the sum of the terms, squares, cube, or other.

Let Us Understand Through An Example:

Missing Number Series Questions

1. Find the missing number 1, 2 6, 24,?

Solution: The given sequence has 4 terms. We will check which rule is applied by picking the first 3 terms. The second number in the sequence is 2 and the first number is 1 which means 1 is either added or 2 has been multiplied to obtain the second term.  The third term is 6 which we got from 2 by multiplying with 3. Hence, now we have 1 x 1, 1 x 2, 2 x 3, and 6 x 4. Thus, we have identified the rule and accordingly, the last term will be 24 x 5= 120.

Hence, the missing number is 120

2. How To Find A Missing Number In a Sequence?

Solution: Here are the steps to find missing numbers in sequence:

1. Identity, if the order of number given is ascending ( smaller to larger number)  or descending ( larger to smaller number)

2.  Calculate the differences between those that are next to each other.

3.  Estimate the difference between numbers to calculate the missing number.

Let us Understand The Above Steps Through An Example:

Find The Missing Number in the Following Sequence 30, 23? 9.

Solution: The numbers given in sequence are in decreasing order. It implies that numbers are arranged from larger to smaller.

The difference between the numbers 30-23=7

As the sequence of the numbers is in decreasing order, subtract 7 from 23. The missing number is 16 as it is 7 more than the previous number 9.

Solved Examples on Missing Numbers

1.  Find the missing number in the following sequence 1, 3, 5, 7, 11, ? 17, 19

Solution: The missing number found in the following sequence is 13.

It is because all the given numbers in the sequence 1, 3, 5, 7, 11, 17, 19 are prime numbers. The numbers given in the sequence are prime numbers as they can be divided only by 1 and itself.

Hence, the number line series will be 1, 3, 5, 7, 11, 13, 17, and 19.

2.  Find the missing number in the following sequence 1, 3, 9, 15, 25,? ,49

Solution: The missing number found in the following sequence is 35.

It is because all the numbers in the sequence are squares and (square-1) such as

12 = 2

22 = 4 and then 4 -1 = 3

32 = 9

42 = 16 and then 16-1 = 15

52 = 25 and

62 = 36 and then 36-1 = 35

72 = 49

Hence, the number line series will be 1, 3, 9, 15, 25, 35, and 49

Quiz Time

1.  Find the missing number 9, 35, 91, 189, 341, ?

      a.   559

      b.   611

      c.   521

      d.  502

2. Find the missing number.

1. 16

2. 52

3. 256

4. 112

3. Find the missing number:

1. 19

2. 24

3. 22

4. 20

Fun Facts

The number zero is first introduced by Aryabhatta.

The numbers 0-9 were introduced in India in the 6th or 7th century and are introduced in Europe through Middle Eastern Mathematician al-Khwarizmi and al-Kindi during the 12th century. These numbers are also known as Arabic Numerals.

How does Vedantu help students to learn about Missing numbers and other relevant topics of math? 

1. Vedantu is a free online learning platform for all students and aspirants to learn about Missing numbers and other important topics of maths.

2. In this regard, Vedantu provides NCERT Texts, NCERT solutions to learn Missing numbers in both English and Hindi medium. Likewise, Vedantu also provides Important questions, Revision notes and keynotes, CBSE Sample question papers and Previous Year's question papers along with the answer key for the students to prepare for the chapter Missing Numbers.

3. Students can also solve questions on Missing Numbers from important Reference books like RD Sharma, RS Aggarwal and HC Sharma solved by the expert teachers in Maths at Vedantu. 

4. Students can also learn more about Missing numbers from the Micro courses available at the website of Vedantu at a pocket friendly amount of 1 rupee per course. Students can also learn about Missing numbers from the Vedantu Mathlete Class 9 Youtube Channel.

5. Junior Students can also learn about Missing numbers in the personalised learning courses of Maths classes for students of age 4 to 14, foundation courses for Class 6 to 8.

6. Students can study about Missing numbers in Personalised Learning from Talented teachers through the Private Home tuitions conducted online in major cities of India and abroad.