Number Series Reasoning Tricks: Missing Number, Wrong Number and Pattern Questions for SSC CGL, CHSL

A number series question gives a list of numbers that follow a hidden rule, and you must find the next number, the missing number or the wrong number. It is a regular question in SSC CGL, CHSL and MTS exams. These number series reasoning tricks for SSC list every common pattern in a table, explain a fast checking order and give solved examples with practice questions.

Common Patterns in Number Series

Checking Order (Save Time)

1. Find the difference between the neighbouring numbers. If it is the same, it is an AP.
2. If the differences change, find the difference of the differences (second-order).
3. If the numbers grow fast, check the ratio of the neighbouring numbers.
4. Compare the numbers with squares (4, 9, 16, 25, 36 ...) and cubes (8, 27, 64, 125 ...).
5. Check the alternate numbers separately.
6. Check prime numbers if the numbers look irregular and odd.

Squares and Cubes to Remember

Solved Examples

Example 1. Find the next number: 2, 5, 10, 17, 26, ?
The differences are 3, 5, 7, 9, so the next difference is 11 and the answer is 26 + 11 = 37.

Example 2. Find the next number: 1, 2, 6, 24, 120, ?
The multipliers are 1, 2, 3, 4, 5, and the next one is 6. The answer is 120 × 6 = 720.

Example 3. Find the next number: 3, 5, 9, 17, 33, ?
Each number is double the previous number minus 1. So 33 × 2 − 1 = 65.

Example 4 (wrong number). Find the wrong number: 2, 6, 18, 54, 160, 486.
Each number is 3 times the previous one. After 54, the number should be 162, so the wrong number is 160.

Example 5. Find the next number: 2, 6, 12, 20, 30, ?
The numbers are 1 × 2, 2 × 3, 3 × 4, 4 × 5, 5 × 6, so the next is 6 × 7 = 42.

Tips for Wrong Number Questions

• First find the rule using the first three or four numbers, which are usually right.
• Then check each number with that rule and find which number breaks it.
• If the series goes up and down, treat the odd and even places as two separate series.

Quick Tips

• Check the difference first, then the ratio, then squares and cubes.
• Learn the squares up to 25 and the cubes up to 10.
• Write the second-order difference when the differences keep growing.
• For the wrong number, find the rule from the numbers at the start.

Quick Revision Points

• AP has a constant difference and GP has a constant ratio.
• Growing differences mean a second-order series.
• Squares: 1, 4, 9, 16, 25 and cubes: 1, 8, 27, 64, 125.
• n(n + 1) gives 2, 6, 12, 20, 30, 42.
• Alternate numbers may be two separate series.

Practice Questions With Answers

1. Find the next number: 7, 14, 21, 28, ?
   Answer: 35
2. Find the next number: 1, 3, 6, 10, 15, ?
   Answer: 21
3. Find the next number: 100, 95, 90, 85, ?
   Answer: 80
4. Find the next number: 2, 4, 8, 16, ?
   Answer: 32
5. Find the next number: 1, 8, 27, 64, ?
   Answer: 125
6. Find the next number: 0, 3, 8, 15, 24, ?
   Answer: 35
7. Find the next number: 4, 9, 19, 39, 79, ?
   Answer: 159
8. Find the next number: 11, 13, 17, 19, 23, ?
   Answer: 29
9. Find the wrong number: 3, 6, 12, 24, 50, 96.
   Answer: 50 (it should be 48)
10. What type of series is 2, 4, 6, 8, 10?
    Answer: An arithmetic series (AP) with a common difference of 2

How to Practise This Chapter

Practise 10 questions every day and write the steps on paper. Then attempt timed sets from our practice papers and the previous year papers page. See all topics on the Reasoning notes page, read the previous topic Clock Angle Reasoning and the next topic Missing Number Reasoning. Also read the Letter, Number and Series note and the Arithmetic Formula Guide.

Frequently Asked Questions

What is a number series?

A number series is a list of numbers that follow a rule, and you have to find the next, missing or wrong number.

How do I solve a number series question fast?

Check the difference, then the ratio, then squares, cubes and alternate numbers.

What is a second-order series?

It is a series in which the differences themselves follow a pattern, such as 3, 5, 7, 9.

What is the pattern of 2, 6, 12, 20, 30?

The numbers are n times (n + 1): 1×2, 2×3, 3×4, 4×5, 5×6.

How do I find the wrong number in a series?

Find the rule from the first few numbers and check which number does not follow it.

Which squares and cubes should I learn?

Learn the squares up to 25 and the cubes up to 10.

What is a prime number series?

It is a series of prime numbers such as 2, 3, 5, 7, 11, 13.

Can a series have two patterns?

Yes. The numbers at odd and even places can follow two different rules.

Is number series asked in SSC exams?

Yes. Series questions are asked in SSC CGL, CHSL and MTS reasoning papers.

How much time should I take for one question?

Less than 40 seconds.

What are the common mistakes?

Checking only the difference and not checking the ratio or the alternate numbers.

How can I improve my speed?

Practise 10 series daily and learn the common patterns table by heart.