Number Series Questions: Every Pattern Type Explained (With Solved Examples)

Published: May 2026 | Covers: CCAT, Cubiks, SHL, PI Cognitive, Matrigma, Caliper, Alva Labs

Number 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.

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 differences
Look for squares, cubes, or Fibonacci patterns
If nothing fits — split the series into odd and even positions

Work 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 = 29

Speed 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 = 96

Speed 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 = 23

Speed 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 = 17

Speed 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 = 63

Speed 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=13

Next term: 8 + 13 = 21

Variation: Fibonacci series do not always start at 1.

Example: 2, 5, 7, 12, 19, 31, ?

Next term: 19 + 31 = 50

Speed 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=5²

Next term: 6² = 36

Variation with constant: 2, 5, 10, 17, 26, ?

1²+1=2, 2²+1=5, 3²+1=10, 4²+1=17, 5²+1=26

Next term: 6²+1 = 37

Speed 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=5³

Next term: 6³ = 216

Reference: 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 = 17

Reference: 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: 3.0

Example 2: 1/2, 1/4, 1/8, 1/16, ? Each term divided by 2 → Geometric Answer: 1/32

Speed 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 apply

Work 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:

Test	Publisher	Number Series?
CCAT	Criteria Corp	✅ Yes — numerical section
Cubiks Logiks General	Talogy	✅ Yes — numerical section
SHL Verify G+	SHL Group	✅ Yes — numerical reasoning
PI Cognitive Assessment	The Predictive Index	✅ Yes — numerical section
Caliper Cognitive	Talogy	✅ Yes — number series questions
Matrigma	Assessio	✅ Indirect — pattern logic
Alva Labs Logic Test	Alva Labs	✅ Indirect — pattern logic
Maersk PLI	The 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:

Disclaimer: This guide is an independent educational resource created by AptitudeAce. It is not affiliated with any test publisher. All examples are original content.

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