Series – Reasoning Ability (District Judge Exam)
Series problems test your ability to spot hidden patterns or rules in a sequence of numbers, letters or symbols and then predict the next element(s).
They are a staple of reasoning tests – the key to success is a systematic approach, not just intuition.
1. Simple Explanation
A series is a list of items (numbers, letters, shapes, etc.) arranged in a definite order.
The goal: find the rule that generates the series and use it to determine the missing/next element(s).
2. Key Points & Common Pattern Types
| Pattern | What to look for | Typical rule |
|---|---|---|
| Arithmetic | Constant difference between successive terms | a, a+d, a+2d, … |
| Geometric | Constant ratio between successive terms | a, ar, ar², … |
| Squares/Cubes | Each term is a perfect square/cube | 1, 4, 9, 16, … |
| Fibonacci / Additive | Each term is sum of previous two | 1, 1, 2, 3, 5, 8, … |
| Alternating pattern | Two or more sub‑patterns interleaved | 1, 2, 4, 3, 9, 5, … |
| Letter series | Alphabet positions, skipping, jumping | A, C, F, J, O, … |
| Prime / Composite | Only primes, only composites, or alternation | 2, 3, 5, 7, 11, … |
| Difference pattern | Look at differences, ratios, or higher‑order differences | 1, 4, 9, 16, … → first diff = 3,5,7… |
| Multiple operations | Addition + subtraction, multiplication + addition, etc. | 2, 6, 10, 18, 22, … (+4, +4, +8, +4) |
| Position‑based patterns | Use term position (1‑st, 2‑nd, …) | 1, 4, 9, 16 → n² |
Tip: When a single rule doesn’t fit, look for alternating or interleaved sub‑series.
3. Systematic Approach
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Write the series clearly.
If the series is long, write down the first 4–6 terms. -
Check for the simplest patterns first.
- Arithmetic → constant difference?
- Geometric → constant ratio?
- Squares/Cubes → perfect powers?
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Analyse differences (or ratios) if the above fail.
- Compute first‑order differences.
- If differences themselves form a pattern, that’s the rule.
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Consider alternating sub‑series.
- Separate odd and even positions, then test each.
-
Try letter positions.
- Convert letters to numbers (
A=1, B=2,…) and repeat steps 2–4.
- Convert letters to numbers (
-
If still stuck, look for “compound” rules:
- Eg. multiply by a number, then add/subtract a fixed amount.
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Test the candidate answers (if options are provided).
- Plug each into the rule and see which satisfies it.
-
Validate with the next term (if there is one).
- Confidence rises when the rule predicts more than one term correctly.
4. Worked Example
Series: 2, 5, 10, 17, 26, ?
Step‑by‑Step
| Term | Value | Difference to previous |
|---|---|---|
| 1 | 2 | – |
| 2 | 5 | 3 |
| 3 | 10 | 5 |
| 4 | 17 | 7 |
| 5 | 26 | 9 |
Observation: The differences are 3, 5, 7, 9 – *