Missing numbers are the numbers that have been skipped out from a particular sequence or series that shows identical variations. We can find such missing numbers by considering the pattern followed by the numbers in the given sequence or series. This pattern can be differences, products, square rules, or a mix of different mathematical operations. Also, these number series might follow a particular rule or formula throughout the entire series.

What are Missing Numbers?

Missing numbers are the numbers that are missed out of a particular sequence or series. These numbers are part of a series with similar changes between those numbers. We can also call missing numbers a part of the sequence of numbers that follow a specified rule, law, or formula.

Missing Number Sequence

In a missing number sequence, you might be asked to locate the missing number anywhere in the series, it can be at the beginning of the series or the end of the series. In such a sequence, the structure lies quite close to the incorrect series. The only thing to be considered is to crack the rule and find the approximate next number in the sequence.

Every missing number series is unique in itself and no specific rule can be followed to find it, we can still generalize some of the common steps to locate the missing number in the series.

• Step 1: Select first 2 or 3 terms to crack the rule of the sequence. This will help in finding the missing number. For instance: if a sequence has 5 terms, we can start with the first three terms and check the rule applied.
• Step 2: Another basic rule to find the missing number is to start with the number that is easy to operate. This includes the terms that are factors of 2, 3, 5 or 10. Also, we can check for squares, cubes and cube roots of numbers to get to a conclusion about the rule.

Solved Examples of Missing Numbers

Example 1: 1, 8, 9, 64, 25, 216,?

Solution: As we can see that the numbers in the given series are in increasing order. So, the rule might include addition or multiplication.

Also, we can check that the numbers displayed are squares and cubes of some number. So, the rule becomes:

 So, the required missing term is 49.

Example 2: 32, 40, 24, 16, 24,?

Solution: As we can see that the third term in the series is less than the first term, the rule followed will include subtraction or division. Similarly, as the second term is greater than the first term, the rule followed will include addition or multiplication.

Taking the reference from the first three terms, we can see that:

32 + 8 = 40, and 32 – 8 = 24

Similarly, the next three terms, 16 + 8 = 24, and 16 – 8 = 8

So, the required missing term is 8.

Example 3: 1, 3, 9, 15, 25, ?, 49

Solution: As the numbers in the series are in increasing order, we can say that the series includes the addition or multiplication of numbers.

Also, when we check the pattern or the rule followed in the numbers, we conclude that:

Alternate numbers are squares of any number and the others are one subtracted from the square.

So, the required missing term is 35.

Example 4: 10, 22, 46, 94, 190, ?

Solution: As the series given is made from increasing numbers so it involved addition or multiplication of numbers.

The pattern followed in the given sequence is 2x + 2.

As, 2(10)+2 = 22, 2(22) + 2 = 46, 2(46) + 2 = 94,…

Following the same pattern, the missing number becomes 2(190) + 2 = 382.

So, the required missing term is 382.

Example 5: 5, 7, 12, 11, 13, 24, 17, 19, ?

Solution: The given sequence follows a pattern where every third number is the sum of the first two numbers:

Like, 5 + 7 = 12, 11 + 13 = 24,…

Similarly, 17 + 19 = 36

So, the required missing term is 36.

Example 6: 2, 3, 6, 4, 5, 20, ?, 3, 18

Solution: In the given sequence we can see that every third term is the product of the proceeding two terms.

Like, 2(3) = 6, 4(5) = 20,…

So, 6(3) = 18.

So, the required missing term is 6.

Example 7: ?, 12, 18, 10, 6, 14, 5, 0, 10

Solution: This number series follows a pattern where each group of three numbers is related by subtraction and addition from a central value.

Let's examine the last three terms:

Like, 5 – 5 = 0, and 5 + 5 = 10

Next three terms:

10 – 4 = 6, and 10 + 4 = 14.

Now, the missing part is the first triplet:

Let the missing number be X
If the second and third terms are 12 and 18, then:
X – 3 = 12 ⇒ X = 15
X + 3 = 18
So, the pattern holds, and the correct missing number is 15.

Example 8: 1, 2, 5, 3, 4, 25, 5, 6, ?

Solution: Looking at the numbers in the series, we can conclude that the third term is made from the combination of the proceeding two terms, like:

So, the required missing term is 61.

Example 9: 5, 7, 11, ?, 17, 19

Solution: The numbers in the given sequence are the prime numbers in their original order. So, we can say that the sequence becomes 5, 7, 11, 13, 17, 19.

So, the required missing term is 13.

Example 10: 1, 2, 6, 24, ?

Solution: As the numbers in the sequence are in increasing order, so we can say that either these numbers are multiplied or added to get the next term of the sequence.

Here, the pattern followed involves the multiplication of the numbers with a natural number in their original order to get the next number.

Like; 1(1) = 1, 1(2) = 2, 2(3) = 6, 6(4) = 24,…

So the last term becomes 24 (5) = 120.

So, the required missing term is 120.

We hope that the above article is helpful for your understanding and exam preparations. Stay tuned to the Testbook App for more updates on related topics from Mathematics, and various such subjects. Also, reach out to the test series available to examine your knowledge regarding several exams.