NISM Banking & SSC, Quantitative Aptitude. Updated Jun 2026, 9-minute read.
Number Series — All Pattern Types for IBPS PO and SSC CGL
Number series questions appear in almost every competitive exam — 5 questions in IBPS PO Prelims, 3–5 in SSC CGL. Recognising the pattern quickly (within 30 seconds per question) is the skill being tested.
Key takeaways
- Arithmetic series: constant difference between consecutive terms (e.g., 3, 7, 11, 15 — diff = +4)
- Geometric series: constant ratio between consecutive terms (e.g., 2, 6, 18, 54 — ratio = ×3)
- Difference-of-difference: 2nd level differences are constant (e.g., 1, 2, 4, 7, 11 — 1st diff: 1,2,3,4; 2nd diff: 1,1,1)
- Fibonacci-type: each term = sum of previous two (e.g., 1, 1, 2, 3, 5, 8, 13)
- Prime number series: 2, 3, 5, 7, 11, 13 — differences are primes or terms are primes
- Alternating series: odd-position and even-position terms follow separate patterns
- Square/cube-based: n², n³, or n² ± constant patterns
How to Approach Number Series
The 30-second rule: spend max 30 seconds per series. If you can't find the pattern in 30 seconds, skip and move on.
Step 1: Check differences (D1)
Calculate consecutive differences: term2 − term1, term3 − term2, etc.
- If differences are constant → Arithmetic series
- If differences are not constant → calculate 2nd order differences (D2)
Step 2: Check 2nd order differences (D2)
D2 = differences between D1 values.
- If D2 is constant → quadratic series (n² type)
- If D2 has a pattern (itself arithmetic) → cubic tendency
- If D2 are themselves an AP → look for n³ or n²±k pattern
Step 3: Check ratios
If differences don't work, try ratios: term2/term1, term3/term2. Constant ratio = Geometric Progression.
Pattern Examples
Type 1: Pure Arithmetic
3, 7, 11, 15, 19, ? → Difference = +4 → Next = 23
Type 2: Geometric
2, 6, 18, 54, 162, ? → Ratio = ×3 → Next = 486
Type 3: Difference of Differences
1, 3, 7, 13, 21, ? → D1: 2, 4, 6, 8 → D2: 2, 2, 2 → D1 next = 10 → Next term = 21+10 = 31
Type 4: Squares
1, 4, 9, 16, 25, ? → n² → Next = 36 (6²)
Variant: 3, 8, 15, 24, 35, ? → (n²−1): 4−1, 9−1, 16−1... → Next = 48
Type 5: Mixed Operations
2, 5, 14, 41, 122, ? → Each term: ×3 − 1 → 122×3 − 1 = 365
Type 6: Alternating
3, 7, 6, 14, 12, 28, 24, ? → Odd positions: ×2 (3,6,12,24...) → Even positions: ×2 (7,14,28...) → Next odd = 48
Type 7: Wrong Number in Series
Exams often ask to find the wrong term. Strategy: find the pattern using 3–4 correct terms, then check which term breaks it.
Example: 2, 3, 7, 22, 89, 446 — each term × previous term − 1: 2×1=2, 3×2=6≠7... Pattern should be ×(n−1)+1. Correct series: 2, 3, 7, 22, 89, 446. Term 3: 3×2+1=7 ✓. Term 4: 7×3+1=22 ✓. Term 5: 22×4+1=89 ✓. Term 6: 89×5+1=446 ✓. So no wrong number here.
Frequently asked questions
How many number series questions come in IBPS PO Prelims?
Typically 5 number series questions appear in IBPS PO Prelims QA section (out of 35 questions). They are usually straightforward — standard arithmetic, geometric, or difference-based patterns. Aim to solve all 5 in 5 minutes maximum.
Should I attempt number series first in the exam?
Many toppers suggest attempting number series early in QA — they're usually quick (20–30 sec per question if you know the pattern). However, if you can't identify the pattern in 30 seconds, skip immediately. Don't let one stubborn series waste 3 minutes.
Written by Arpan Das.
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