Number sequence (number series) items show a list of numbers and ask for the next term or a missing term. They are part of Numerical Ability on both the Professional and Subprofessional CSE-PPT. The good news: most series follow a handful of patterns. Learn to test those patterns in order and these become some of the fastest points on the paper.
Key takeaways
- Most series are arithmetic, geometric, growing-gap, alternating, Fibonacci-style, or squares/cubes.
- Always check differences first, then ratios, then alternating positions.
- Write the differences under the series — seeing the second row is often the whole answer.
- Confirm your rule on every given term before choosing an option.
- If you cannot find the rule in about a minute, flag it and come back.
The six patterns to know
| Pattern | How it works | Example | Next |
|---|---|---|---|
| Arithmetic | Add or subtract the same number | 7, 11, 15, 19 | 23 (+4) |
| Geometric | Multiply or divide by the same number | 3, 6, 12, 24 | 48 (×2) |
| Growing gap | Differences themselves follow a pattern | 2, 3, 5, 8, 12 | 17 (+1, +2, +3, +4, +5) |
| Alternating | Two series interleaved, or two operations taking turns | 1, 10, 2, 20, 3, 30 | 4 |
| Fibonacci-style | Each term is the sum of the two before | 2, 3, 5, 8, 13 | 21 |
| Squares and cubes | Terms are n², n³, or close to them | 1, 4, 9, 16, 25 | 36 |
A step-by-step method
- Write the differences. Constant gap → arithmetic. Gaps that grow by a steady amount → growing gap.
- Check ratios. If each term is a multiple of the last, try ×2, ×3, ÷2.
- Split odd and even positions. If the series jumps up and down, it may be two series in one.
- Look for famous numbers. Squares (1, 4, 9, 16…), cubes (1, 8, 27, 64…), and primes (2, 3, 5, 7, 11…).
- Verify on the last given term. The right rule must produce every term you were given, not just the first few.
Worked example
Stem: 5, 8, 14, 23, 35, ?
- A.44
- B.48
- C.50
- D.53
Work: Differences: 8−5=3, 14−8=6, 23−14=9, 35−23=12. The gaps increase by +3 each time, so the next gap is 15. 35+15 = 50. Answer: C. 50.
Quick practice
- 81, 27, 9, 3, ?
- A.0
- B.1
- C.2
- D.6
Answer: B — Divide by 3 each time: 3÷3=1.
- 4, 5, 9, 14, 23, ?
- A.28
- B.37
- C.32
- D.41
Answer: B — Each term is the sum of the previous two: 14+23=37.
- 2, 9, 4, 16, 6, 25, 8, ?
- A.10
- B.30
- C.36
- D.49
Answer: C — Two series: 2, 4, 6, 8 and 9, 16, 25, 36 (squares of 3, 4, 5, 6).
- 1, 8, 27, 64, ?
- A.81
- B.100
- C.125
- D.128
Answer: C — Cubes: 1³, 2³, 3³, 4³, so next is 5³ = 125.
- 100, 95, 85, 70, 50, ?
- A.20
- B.25
- C.30
- D.45
Answer: B — Differences −5, −10, −15, −20, so next is −25: 50−25 = 25.
Common traps
- Forcing ×2. Assuming every fast-growing series is doubling when the differences tell the real story.
- Ignoring the last gap. Finding a rule that fits the first terms but fails on the final given term.
- Two-sequence blindness. Missing that a jumpy series is really two simple series interleaved.
- Sign errors. Losing a minus when the series decreases.
- Option shopping. Picking the number that "looks close" without stating a rule.
Frequently asked questions
Is number sequence on both Professional and Subprofessional?
Yes. Number sequence is listed under Numerical Ability, which appears on both levels of the CSE-PPT.
How do you solve number series questions quickly?
Check differences first, then ratios, then alternating positions. Most items fall to one of these three checks within a minute.
What if no pattern works?
Look for squares, cubes, primes, or a Fibonacci-style sum. If nothing fits within about a minute, eliminate options that break obvious trends, choose, flag it, and move on.
Can I use a calculator for number series?
No. CSC prohibits calculators at the examinee's seat, so practice mental arithmetic with these patterns.
Study with this product
- Take the free diagnostic to see if this topic is a weakness.
- Drill Number sequence in Practice, or use Today's plan for short pattern bursts.
- Take a full mock when the app recommends one so you don't overinvest time on one stubborn series.
Honest facts
- This guide is a study aid, not an official CSC reviewer and not a pass promise.
- We never invent official CSC dates, fees, or room assignments.
- Sample stems here are original practice items for skill-building, not leaked exam content.
- Readiness Score is a product metric — not a CSC rating prediction.
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