# Missing Numbers

## Number series

A series or sequence where a number is missed is known as a missing number sequence. The number series may have a specific pattern, like similar differences, products, square rules, or any other mathematical pattern. In addition, the number series may have a particular formula or rule that might be followed in the entire number sequence.

## How to find a missing number in a sequence?

To find a missing number in a particular sequence, we must identify the pattern of the series. The pattern can be anything. We need to study and apply all possible mathematical expressions to find the pattern in the given number sequence. In finding a missing number type of question, we are asked to find the missing number in the starting, in the middle, or maybe at the end.

Example 1: Find the missing number in the sequence 30, 23, ?, 9.
Solution:

We can see the numbers in the sequence are in decreasing order. The difference between the numbers 30 – 23 = 7.
We can see the numbers are having a difference of 7 and are decreasing order. Therefore, subtracting 7 from 23, we get 16, which is the missing number in the series.

Example 2: Find the missing number in the sequence 1, 3, 5, 7, 11, ? 17, 19
Solution:

We can observe, all these numbers are prime numbers. Therefore, the missing number is a prime number between 11 and 17. Do we know the prime number that exists between 11 and 17? The missing number is 13.

Example 3: Find the missing number in the sequence 1, 3, 9, 15, 25,? ,49
Solution:

The given sequence comprises alternate squares and (squares – 1). This means the sequence is 12 = 1, 22 – 1 = 3, 32 = 9, 42 – 1 = 15 …
By this sequence, the missing number is 35.

Example 4: Write the missing number in the sequence 2, 3, 6, 4, 5, 20, ? , 3, 18.
Solution:

This is a product sequence. The product of 2 and 3 is 6, and the product of 4 and 5 is 20. However, we see the number decreases to 18, which means, the product of 3 and 6 must be 18. Hence, the missing number is 6.

Example 5: Find the missing number in the sequence 1, 2, 5, 3, 4, 25, 5, 6, ?
Solution:

We see the summation of squares of the numbers 1 and 2 = 5, i.e., 12 + 22 = 5. Similarly, 32 + 42 = 25. Therefore, the missing number must be the result of 52 + 62 = 61.
Hence, the missing number is 61.

Example 6: Find the missing number in the sequence 5, 7, 12, 11, 13, 24, 17, 19, ?
Solution:

We see, the sequence is of prime numbers and their sum. For example, 5 and 7 are prime numbers and their sum is 12. The next prime numbers are 11 and 13, and their sum is 24. Similarly, 17 and 19 are next prime numbers, their sum is 36.
Therefore, the missing number is 36.

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