 # Missing Numbers

## 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 Question

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

### How To Find A Missing Number In a Sequence?

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

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, ?

1. 559

b.   611

c.   521

d.  502

2. Find the Missing Number

 4 16 ? 64

1. 16

2. 52

3. 256

4. 112

3.  Find the Missing Number

 8 3 21 6 5 25 12 2 ?

1. 19

2.  24

3. 22

4. 20

### Fun Facts

• The number zero is first introduced by Aryabhatta.

• The numbers 0-9 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.

1. What are known as sequences and series?

A sequence is a grouping of any objects or a set of numbers in a specific order along with some rules. If x1, x2, x3, x4………etc. represent the terms of sequence then 1,2,3,4 represent the position of the term.

A sequence is defined on the basis of the number of terms that are either finite sequence or infinite sequence.

A series is defined as the sum of all the terms in a sequence.

For example: If x1, x2, x3, x4 is a sequence, then its equivalent series is given by

Sn = x1+ x2+ x3+ x4….+ xn

Note: The given series is either finite or infinite depending if the sequence is finite or infinite.

2.  What are the different types of sequences and series?

The different type of sequences and series are:

1.      Arithmetic sequence

2.      Harmonic sequence

3.      Geometric sequence

4.      Fibonacci sequence

Arithmetic Sequence

A sequence in which each term is obtained by adding or subtracting a definite number to the previous number is known as the arithmetic sequence.

Harmonic sequence

A series of a number in which the reciprocals of all the terms of the sequence forms an arithmetic sequence is known as a harmonic sequence.

Geometric Sequence

A series in which each term is obtained by dividing or multiplying a definite number to the previous number is known as the geometric sequence.

Fibonacci sequence

A sequence in which each number is obtained by adding two previous terms and the sequence starts with 0 and 1 is known as the fibonacci sequence. Sequence is represented by F0 = O and F1= 1 and Fn = Fn-1 + Fn-2