Missing numbers in the sequence | Know Your Aptitude Class 6 To 8 - Class 8 PDF Download

Missing Numbers

Missing numbers are the numbers that got missed in the given series of numbers with similar differences among them. The process of writing the missing numbers is termed as finding similar changes between those numbers and filling their missing values in their specific series and places. 

Missing Number Problems

Example 1: Write the missing number in the given sequence.
2, 3, 6, 4, 5, 20, ? , 3, 18.

Ans: The missing number is found to be as 6.
This is because a relationship between the numbers in the given series is determined as the third digit ‘6’ which is the product of the first two digits ‘2’ and ‘3’, the sixth digit ‘20’ is the product of fourth digit ‘4’ and fifth digit ‘5’ and the ninth digit ‘18’ is the product of the seventh digit ‘6’ and eighth digit ‘3’.
Therefore, the seventh digit should be “6”.
The series is 2, 3, 6, 4, 5, 20, 6, 3, 18.

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

Ans: The missing number is found to be 35
This is because all the sequence of numbers are squares and (squares – 1) alternatively like
1 square = 1,
2 square = 4 and then 4 – 1 = 3,
3 square = 9,
4 square = 16 and then 16 – 1 = 15,
5 square = 25,
6 square = 36 and then 36 – 1 = 35
7 square = 49.
Therefore, the number line will be 1, 3, 9, 15, 25, 35, 49.

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

Ans: The missing number is found to be 13.
This is because all the given orders of numbers in a number line contain the prime numbers 5, 7, 11, 13, 17, 19 which are all divisible by only ‘1’ and itself.
Therefore, the number line series will be 5, 7, 11, 13, 17, 19.

Steps for Finding Missing Numbers in Arithmetic Sequences

• Step 1: Find the common difference of each pair of consecutive terms in the sequence by subtracting each term from the term that comes directly after it.
• Step 2: Add the common difference to the number prior to the first missing number in the sequence.
• Step 3: Repeat Step 2 for any other missing numbers.
• Step 4: Check your answer by adding the common difference to each term in the sequence to ensure that the result is the next term in the sequence.