How to Find Missing Numbers

Missing numbers problems are a common and fundamental aspect of mathematics, particularly in fields such as arithmetic, algebra, and statistics. These problems involve identifying one or more numbers that are missing from a sequence, equation, or data set. They help develop critical thinking, pattern recognition, and problem-solving skills. In this article we will learn what are missing numbers, patterns in missing numbers, solved examples based on them and also practice questions based on them.

What are Missing Numbers?

This is a kind of math riddle that falls under the "missing number" category, in which one or more numbers are lacking from a sequence or equation; it's also tasked to find what those lost figures could be based on available information. Such problems are often used in the educational setting to develop thinking skills, pattern recognition and general problem solving. Identifying missing numbers is crucial in developing a deeper understanding of number patterns, sequences, and algebraic thinking.

Methods to Find Missing Numbers

There are several methods to find missing numbers. These methods are discussed in detail below:

Arithmetic Sequences

Imagine a string of numbers where the gap between each pair of consecutive terms is the same.

Example: Can you figure out the missing number in this sequence: 2, 5, _, 11?

Well, to find it, you can calculate the difference between the numbers, which is 3 in this case. Then, just add that difference to the previous number, 5, and you get the missing term: 8.

Geometric Sequences

A geometric sequence is a sequence where each term is found by multiplying the previous term by a fixed, non-zero number called the ratio.

Example: Find the missing number in the sequence: 3, 9, _, 81.

• Ratio (r) = 9 / 3 = 3
• Missing number = 9 × 3 = 27

Patterns in Numbers

Recognizing patterns helps in predicting the next number or identifying missing elements.

Example: Find the missing number in the sequence: 1, 4, 9, _, 25.

• The pattern is n^2.
• 1 = 1², 4 = 2², 9 = 3², 25 = 5²
• Missing number = 4² = 16

Tips and Tricks to Find Missing Numbers

There are following tips and tricks to find missing numbers.

• Identify the Pattern: Look for common differences, ratios, or other recognizable patterns.
• Write Down Observations: Writing out what you observe can help clarify the pattern.
• Check Your Work: Verify by plugging the missing number back into the sequence.
• Use Algebra: For more complex sequences, set up and solve equations.
• Practice Regularly: Consistent practice with various types of sequences improves skills.

Solved Examples on Missing Numbers

There are following solved examples based on different pattern of missing numbers.

Example 1: Arithmetic Sequence

Find the lost or missing number in this series:10, 15, __, 25.

• Difference (d) = 5
• Missing number = 15 + 5 = 20

Example 2: Geometric Sequence

Find the lost or missing number in this array: 2, 6..., 54.

• Ratio (r) = 6 / 2 = 3
• Missing number = 6 × 3 = 18

Example 3: Number Pattern

Find the lost or missing number in the sequence of the numbers: 2, 4, 8, 16, _.

• Pattern: Each number is double the previous one.
• Missing number = 16 × 2 = 32

Example 4: Mixed Sequence

Find the lost or missing number in the sequence of the numbers: 5, 10, 20, _, 80.

• Pattern: Each number is double the previous one.
• Missing number = 20 × 2 = 40

Example 5: Arithmetic Sequence

Problem: Find the missing number in the sequence: 7, 15, .. , 31.

Difference (d) = 15 - 7 = 8

Missing number = 15 + 8 = 23

Example 6: Geometric Sequence

Problem: Find the missing number in the sequence: 3, 12, _, 192.

• Ratio (r) = 12 / 3 = 4
• Missing number = 12 × 4 = 48

Example 7: Number Pattern

Problem: Find the missing number in the sequence: 2, 3, 5, 8, 12, ... .

Pattern: The difference between consecutive terms increases by 1 each time.

• 3 - 2 = 1
• 5 - 3 = 2
• 8 - 5 = 3
• 12 - 8 = 4
• The next difference should be 5.
• Missing number = 12 + 5 = 17

Also, Check

• Arithmetic progression
• Geometric Progression
• Arithmetic Operations

Practice Questions on Missing Numbers

Q1: Find the missing number in the sequence: 18, 29, _, 51

Q2: Find the missing number in the sequence: 4, 20, _, 500.

Q3: Find the missing number in the sequence: 1, 2, 6, 24, _, 720.

Q3: Solve for z: 3z + 5 = 2(z + 4)

Q4: Find the missing number in the sequence: 7, 21, 63, _, 567.