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
What is the next number in the series: 2, 5, 10, 17, 26, ?
Practice 5easy
Find the missing term: 100, 99, 97, 94, 90, ?, 79
Practice 6easy
Find the missing number in the series: 2, 6, 12, 20, 30, ?, 56
Practice 7medium
A number series follows the pattern where each term is the sum of the two preceding terms. If the 3rd term is 8 and the 4th term is 13, what is the 6th term?
Practice 8medium
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 9medium
In a series, the nth term is given by the formula T(n) = n² + 2n − 1. What is the difference between the 7th term and the 5th term?
Practice 10medium
A series has the pattern: 3, 6, 12, 24, ... Each term is multiplied by 2 to get the next term. If this pattern continues, what is the 8th term?
Practice 11medium
A series is defined as: 2, 5, 10, 17, 26, ... What is the next term in this series?
Practice 12medium
In a number series, the pattern is: 1, 4, 9, 16, 25, ... followed by 36, 49, 64, ... A new series is formed by taking the difference between consecutive terms of the original series. What is the 5th term of the new series?
Practice 13hard
A series is formed where aₙ = aₙ₋₁ + n². If a₁ = 1, find a₆.
Practice 14hard
A series is defined by the recurrence relation aₙ = 3aₙ₋₁ - 2aₙ₋₂ with a₁ = 2 and a₂ = 5. If the series continues indefinitely, what is the value of a₇?
Practice 15hard
In a series, the nth term is defined as aₙ = n² + 5n + 6. A new series is formed by taking the difference between consecutive terms of the original series. What is the sum of the first 10 terms of this new difference series?
Practice 16hard
A number series has the property that the sum of the first n terms is Sₙ = 2n² + 3n. What is the 8th term of the series?
Practice 17hard
In a series, each term is the product of its position and the sum of all previous terms. If a₁ = 1, what is a₅?
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