Number Series Questions: Every Pattern Type Explained (With Solved Examples) Published: May 2026 | Covers: CCAT, Cubiks, SHL, PI Cognitive, Matrigma, Caliper, Alva LabsNumber series questions appear in almost every pre-employment aptitude test — including the CCAT, Cubiks Logiks, SHL Verify G+, PI Cognitive Assessment, Matrigma, Caliper, and Alva Labs Logic Test. Regardless of which test you are facing, the underlying pattern types are identical.The good news: there are only 10 pattern types. Once you recognise all of them, no number series question can surprise you on test day.This guide covers every type with one fully solved example, a speed tip for each, and a master checklist you can apply to any question.If you are preparing for one of these tests, see our complete guides: CCAT, Cubiks, SHL, PI Cognitive, Caliper. Benchmark your current pace → Free 5-minute CCAT test How to Approach Any Number Series Question Before looking at individual types, apply this universal checklist to every question — in this exact order:Check the differences between consecutive terms — are they constant?Check the ratios — is each term multiplied or divided by the same number?Check the differences of the differencesLook for squares, cubes, or Fibonacci patternsIf nothing fits — split the series into odd and even positionsWork through these five steps in order and you will identify the pattern within 30 seconds on almost any number series question. Type 1 — Arithmetic Series Rule: Each term increases or decreases by a constant number.Example: 4, 9, 14, 19, 24, ?Solution: Differences: 9−4=5, 14−9=5, 19−14=5, 24−19=5 Constant difference of 5 → Arithmetic series Next term: 24 + 5 = 29Speed tip: Always check differences first. If they are all equal, you are done in under 5 seconds. Type 2 — Geometric Series Rule: Each term is multiplied or divided by a constant number.Example: 3, 6, 12, 24, 48, ?Solution: Differences: 3, 6, 12, 24 — not constant. Check ratios. 6÷3=2, 12÷6=2, 24÷12=2, 48÷24=2 Constant ratio of 2 → Geometric series Next term: 48 × 2 = 96Speed tip: When differences keep growing rapidly, think multiplication before anything else. Type 3 — Two-Stage / Double Difference Series Rule: The differences between terms are not constant — but the differences of those differences are.Example: 2, 3, 5, 8, 12, 17, ?Solution: First differences: 1, 2, 3, 4, 5 Second differences: 1, 1, 1, 1 — constant Next difference: 6 Next term: 17 + 6 = 23Speed tip: When differences are growing steadily but not by multiplication, go one level deeper and check the differences of the differences. Type 4 — Alternating Series Rule: The series is actually two separate series interleaved into one.Example: 3, 8, 6, 11, 9, 14, 12, ?Solution: No single rule fits — split into positions. Odd positions: 3, 6, 9, 12 → +3 each time Even positions: 8, 11, 14 → +3 each time Next term is in even position: 14 + 3 = 17Speed tip: Whenever no single rule fits the full series, immediately split into odd and even positions. Type 5 — Mixed Operations Series Rule: Each term is calculated using two operations combined — for example multiply then add.Example: 1, 3, 7, 15, 31, ?Solution: Differences: 2, 4, 8, 16 — doubling but not a pure geometric series. Try: previous term × 2 + 1 1×2+1=3, 3×2+1=7, 7×2+1=15, 15×2+1=31 Next term: 31 × 2 + 1 = 63Speed tip: When differences are doubling but ratios do not cleanly work, try multiplying by a constant then adding a constant. Type 6 — Fibonacci Series Rule: Each term is the sum of the two terms before it.Example: 1, 1, 2, 3, 5, 8, 13, ?Solution: 1+1=2, 1+2=3, 2+3=5, 3+5=8, 5+8=13Next term: 8 + 13 = 21Variation: Fibonacci series do not always start at 1.Example: 2, 5, 7, 12, 19, 31, ?Next term: 19 + 31 = 50Speed tip: When differences keep growing with no fixed pattern, add the two previous terms. Type 7 — Squares Series Rule: Terms are squares of consecutive integers, sometimes with a constant added.Example: 1, 4, 9, 16, 25, ?Solution: 1=1², 4=2², 9=3², 16=4², 25=5²Next term: 6² = 36Variation with constant: 2, 5, 10, 17, 26, ?1²+1=2, 2²+1=5, 3²+1=10, 4²+1=17, 5²+1=26Next term: 6²+1 = 37Speed tip: Large growing jumps between terms — think squares first, then try adding a constant. Type 8 — Cubes Series Rule: Terms are cubes of consecutive integers.Example: 1, 8, 27, 64, 125, ?Solution: 1=1³, 8=2³, 27=3³, 64=4³, 125=5³Next term: 6³ = 216Reference: Memorise the first eight cubes — 1, 8, 27, 64, 125, 216, 343, 512.Speed tip: Very large jumps that squares cannot explain — try cubes. Type 9 — Prime Number Series Rule: Terms are consecutive prime numbers.Example: 2, 3, 5, 7, 11, 13, ?Solution: All prime numbers in ascending order.Next prime after 13 = 17Reference: Memorise the first 15 primes — 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47.Speed tip: Irregular differences but every term is only divisible by 1 and itself — think prime series. Type 10 — Fraction and Decimal Series Rule: Same patterns as arithmetic and geometric — do not let the format distract you.Example 1: 0.5, 1.0, 1.5, 2.0, 2.5, ? Constant difference of 0.5 → Arithmetic Answer: 3.0Example 2: 1/2, 1/4, 1/8, 1/16, ? Each term divided by 2 → Geometric Answer: 1/32Speed tip: Never change your approach for fractions or decimals. Apply the same checklist. The Master Checklist — Apply to Every Question Use this in order every time:✅ Constant difference? → Arithmetic✅ Constant ratio? → Geometric✅ Differences growing steadily? → Two-stage✅ No single rule fits? → Alternating✅ Differences doubling, ratios fail? → Mixed operations✅ Each term = sum of two previous? → Fibonacci✅ Squares or cubes of integers? → Squares / Cubes✅ All terms prime? → Prime series✅ Fractions or decimals? → Same rules applyWork through this checklist in order and you will identify any number series pattern within 30 seconds. Which Pre-Employment Tests Include Number Series? Number series questions appear across all the major pre-employment cognitive assessments:TestPublisherNumber Series?CCATCriteria Corp✅ Yes — numerical sectionCubiks Logiks GeneralTalogy✅ Yes — numerical sectionSHL Verify G+SHL Group✅ Yes — numerical reasoningPI Cognitive AssessmentThe Predictive Index✅ Yes — numerical sectionCaliper CognitiveTalogy✅ Yes — number series questionsMatrigmaAssessio✅ Indirect — pattern logicAlva Labs Logic TestAlva Labs✅ Indirect — pattern logicMaersk PLIThe Predictive Index✅ Yes — numerical section How to Practise Number Series Effectively Three principles that make practice sessions actually useful:1. Practice under timed conditions from the start In a real aptitude test you have 12–18 seconds per question. Practicing without a timer gives false confidence. Always set a timer.2. Review wrong answers carefully The goal is not to get the right answer — it is to understand why the pattern works. If you guessed correctly, still check the working. If you got it wrong, identify exactly which step in the checklist you missed.3. Track which types trip you up After each practice session note which pattern types took longest or produced errors. Most candidates are slow on Two-Stage and Mixed Operations — not because they are harder, but because they require going one step beyond the obvious. Free Number Series Practice Tests Practise with full-length timed tests that include number series questions:CCAT Practice Tests — 6 full-length tests, 300 questionsCubiks Logiks Practice Tests — 6 full-length testsPI Cognitive Assessment Practice TestsCaliper Practice Questions — 150 questions with explanationsSHL Verify G+ Practice TestsDisclaimer: This guide is an independent educational resource created by AptitudeAce. It is not affiliated with any test publisher. All examples are original content. Full Preparation Course CCAT Practice Test Course 6 full-length mocks · 300 questions 247 candidates preparing this week 6 timed full-length mock exams 300 questions with worked solutions Immediate answer explanations 5.0 · 10,000+ candidates prepared "Went from scoring 19 to 34 in one week. Got the offer at Zendesk." — Sarah K., hired at Zendesk Start Full Course → Avg. score improvement +10 points CCAT Full Course 6 mocks · 300 questions View Course ×
