Reasoning Ability – Series
Program: Chandigarh Patwari / Lekhpal
Exam: Reasoning Ability – Series
Series problems test your ability to spot patterns, relationships and rules in a given set of numbers, symbols or figures.
They are the most common and high‑scoring questions in reasoning sections.
1. Simple Explanation
A series is a sequence of items (numbers, letters, shapes, etc.) arranged in a particular order.
In a series question you are given a few terms and must predict the next term(s) or find a missing term.
The key to solving series questions is:
- Identify the rule – arithmetic, geometric, alternating, factorial, Fibonacci, position‑based, etc.
- Apply the rule to the next position.
- Validate that the rule works for all given terms.
2. Key Points to Remember
| Pattern Type | Common Rule | Typical Examples |
|---|---|---|
| Arithmetic Series | Difference between consecutive terms is constant (d). |
3, 7, 11, 15 … (d = +4) |
| Geometric Series | Ratio between consecutive terms is constant (r). |
2, 6, 18, 54 … (r = ×3) |
| Fibonacci / Additive | Each term = sum of previous one or two terms. | 1, 1, 2, 3, 5, 8 … |
| Alternating Series | Two (or more) interleaved sub‑series. | 1, 4, 2, 5, 3, 6 … |
| Multiplication by Position | Term = position × constant or pattern. | 1, 4, 9, 16 … (n²) |
| Digit/Letter Pattern | Each term is derived from digits/letters of previous terms. | 12, 24, 48, 96 … (×2) |
| Cyclic/Repeating Pattern | Sequence repeats after a fixed period. | 1, 2, 3, 1, 2, 3 … |
| Factorial / Combination | Terms involve factorials or combinatorial numbers. | 1, 2, 6, 24, 120 … (n!) |
| Prime / Composite Pattern | Terms are primes, composites, or follow prime gaps. | 2, 3, 5, 7, 11 … |
| Mixed / Hybrid | Combination of two or more simple rules. | 1, 4, 2, 9, 3, 16 … (n² interleaved with n) |
Quick Tips for Every Question
- Write down the series clearly, label positions
n = 1, 2, 3 …. - Check differences (
Δ = a₂ – a₁,a₃ – a₂, …). - Check ratios (
a₂ / a₁,a₃ / a₂, …). - Look for squares, cubes, factorials or known sequences (Fibonacci, triangular numbers).
- Test alternate terms – sometimes the odd and even positions follow separate rules.
- Consider “digit‑sum” or “reverse digits” patterns.
- Validate the rule across all given terms; if it fails, try a different rule.
3. Worked Example
Question:
4, 9, 19, 39, 79, ?
Find the missing term.
Step‑by‑Step Solution
| Term | n | Value | Δ = value – previous |
|---|---|---|---|
| a₁ | 1 | 4 | – |
| a₂ | 2 | 9 | 5 |
| a₃ | 3 | 19 | 10 |
| a₄ | 4 | 39 | 20 |
| a₅ | 5 | 79 | 40 |
| a₆ | 6 | ? | ? |
Observation:
The differences are: 5, 10, 20, 40 – each time doubling.
Therefore the next difference is 40 × 2 = 80.
Add this to the last term:
79 + 80 = 159.
Answer: 159.
Why this works
- The series is not arithmetic or geometric.
- The key was to look at the differences and spot a pattern (powers of 2).
- Once the rule is determined, apply it to the next step.
4. Quick Revision Summary
| Question | Quick Check |
|---|---|
| 1. Identify the rule | Δ or ratio; look for constant, doubling, halving |
| 2. Alternate terms | Separate sub‑series for odd/even positions |
| 3. Digit tricks | Sum of digits, reverse, product of digits |
| 4. Known sequences | Fibonacci, primes, squares, cubes, factorials |
| 5. Mixed patterns | Test two rules; check if both hold for all terms |
| 6. Validate | Apply the rule to all given terms; if any fails, backtrack |
Practice Tip:
Create your own series and try to solve them. The more patterns you familiarize yourself with, the faster you’ll spot them in exams.
5. Mini‑Practice Set
| # | Series | Missing Term | Hint |
|---|---|---|---|
| 1 | 2, 6, 12, 20, 30, ? | ? | Δ = 4, 6, 8, 10, … |
| 2 | 1, 4, 9, 16, 25, ? | ? | n² |
| 3 | 3, 5, 9, 17, 33, ? | ? | Each term = previous × 2 + 1 |
| 4 | 2, 4, 8, 32, 256, ? | ? | Multiply by increasing powers of 2 |
| 5 | 1, 2, 6, 24, 120, ? | ? | n! |
Answers: 42, 36, 65, 4096, 720
Final Thought
Series questions are all about pattern recognition.
With a systematic