Core ConceptRead this first — the foundation of the topic
Arithmetic Series
Each term increases or decreases by a constant difference
Example
5, 8, 11, 14 (difference = +3)
2
Geometric Series
Each term is multiplied by a constant ratio
Example
2, 6, 18, 54 (ratio = ×3)
3. Square/Cube Series: Based on squares or cubes of consecutive numbers
Example
1, 4, 9, 16 (1², 2², 3², 4²)
4
Prime Number Series
Following prime number sequence
5
Mixed Operations
Combination of addition, subtraction, multiplication, division
6. Double/Triple Layer Series: Two or three different patterns running simultaneously
Exam PatternsWhat examiners ask — read before attempting PYQs
SSC CGL typically asks 2-3 questions on number series. Common question types include finding the missing term, identifying the wrong number, or completing the series. The difficulty ranges from simple arithmetic progressions to complex mixed operation patterns.
Powerful Shortcut - The Difference Method:
Write differences between consecutive terms. If first-level differences don't show pattern, find second-level differences (differences of differences).
Most SSC series get solved within 2-3 levels.
Worked ExampleSolve this step-by-step before moving on
Observe the difference pattern
4, 8, 16, ?, ?
This is a geometric series with ratio 2
Next difference = 16 × 2 = 32
Following difference = 32 × 2 = 64
3
Step 3
Find the missing number
? = 31 + 32 = 63
Verify: 127 - 63 = 64 ✓
Answer: 63
ShortcutsUse these to save 30–60 seconds per question
for Square Series:
If you see numbers like 2, 5, 10, 17, 26, check if they follow n² + 1 pattern:
1² + 1 = 2
2² + 1 = 5
3² + 1 = 10
4² + 1 = 17
5² + 1 = 26
Exam TrapsCommon mistakes students make — avoid these
Students often assume the first pattern they see is correct. Always verify your answer by checking if it fits the complete series. In mixed operation series, don't stop at first-level differences - go deeper if needed.
Key Points to Remember
Number series questions appear 2-3 times in SSC CGL with moderate to high difficulty
Use difference method: find differences between consecutive terms to identify pattern
Arithmetic series have constant difference, geometric series have constant ratio
Square series follow pattern n², n²+1, n²-1, or similar variations
Prime number series: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29...
Mixed operation series combine addition, subtraction, multiplication, division patterns
Double layer series have two different patterns running simultaneously
Always verify your answer by checking if it satisfies the complete series pattern
Exam-Specific Tips
First 10 prime numbers: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29
Perfect squares up to 15²: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225
Perfect cubes up to 10³: 1, 8, 27, 64, 125, 216, 343, 512, 729, 1000
Find the next number in the series: 5, 10, 20, 40, 80, ?
Practice 2easy
What is the next number in the series: 1, 4, 9, 16, 25, ?
Practice 3easy
Find the missing number in the series: 100, 90, 81, 73, 66, ?
Practice 4easy
What is the missing number in the series: 3, 6, 12, 24, 48, ?
Practice 5easy
Find the next term in the series: 2, 5, 10, 17, 26, ?
Practice 6easy
What is the next term in the series: 2, 3, 5, 8, 12, ?
Practice 7medium
In a number series, the first term is 5 and each subsequent term is obtained by multiplying the previous term by 2 and then subtracting 3. What is the 5th term of this series?
Practice 8medium
In a series, the nth term is given by the formula: aₙ = n² + 2n − 1. What is the difference between the 5th term and the 3rd term?
Practice 9medium
A series starts with 100 and each term is 80% of the previous term. What is the 4th term of this series (rounded to the nearest integer)?
Practice 10medium
In a series, the difference between consecutive terms increases by 1 each time. The first term is 2, and the second term is 3. What is the 6th term?
Practice 11medium
A series is defined as: 3, 6, 12, 24, 48, ... What is the sum of the 6th and 7th terms of this series?
Practice 12medium
A number series follows the pattern where each term is the sum of the previous two terms. If the 3rd term is 8 and the 4th term is 13, what is the 1st term?
Practice 13hard
A series is defined as: a₁ = 2, and a(n) = a(n-1) + n² for n ≥ 2. What is the value of a₆?
Practice 14hard
A series has the property that each term (starting from the third) is the sum of the two preceding terms multiplied by a constant k. If a₁ = 1, a₂ = 2, a₃ = 9, and a₄ = 33, what is a₅?
Practice 15hard
In a series, the difference between consecutive terms follows a pattern: 2, 6, 12, 20, 30, ... If the first term is 5, what is the 7th term of the original series?
Practice 16hard
A number series follows the pattern where each term is obtained by multiplying the previous term by a constant and then adding a fixed value. If the first term is 3, the second term is 7, and the third term is 15, what is the fifth term of this series?
60-Second Revision — Number Series
Remember: Apply difference method first - find differences between consecutive terms
Formula: For arithmetic series, nth term = a + (n-1)d where a=first term, d=common difference
Trick: If first differences don't work, try second-level differences immediately
Pattern: Check for squares (n²), cubes (n³), or modified versions (n²±k)
Trap: Don't assume first pattern you see is correct - always verify with complete series
Speed: Memorize first 15 squares, 10 cubes, and 10 prime numbers
Strategy: For geometric series, check if ratio is consistent throughout the sequence