Uttarakhand PSC – Reasoning Ability
Topic: Series
Series are sequences of numbers, letters or symbols that follow a specific rule.
The key to solving them is identifying the hidden pattern and then applying it to find the missing or next term.
1. Simple Explanation
| What | How | Why |
|---|---|---|
| Series | A list of items (numbers, letters, shapes, etc.) that are arranged in a particular order. | To test logical thinking, pattern recognition and mental agility. |
| Pattern | A rule that governs how each term is generated from the previous one(s). | Knowing the rule lets you predict all future terms. |
2. Types of Series
| Series Type | Typical Pattern | Example |
|---|---|---|
| Number Series | Linear (add/subtract), Geometric (multiply/divide), Quadratic (square/cube), Alternating, Prime/Composite, Fibonacci, etc. | 2, 5, 10, 17, … |
| Letter Series | Alphabetic shift, skipping letters, reverse order, alternating case, etc. | A, D, G, J, … |
| Mixed Series | Numbers & letters together, or numbers with operations. | 1A, 2B, 3C, … |
| Visual/Shape Series | Pattern of shapes, colors, or digits displayed visually. | (Not covered here) |
3. Key Points & Strategies
| # | Strategy | What to Do | Example |
|---|---|---|---|
| 1 | Look for arithmetic difference | Compute the difference between consecutive terms. | 3, 6, 11, 18 → diffs 3, 5, 7 |
| 2 | Check for geometric ratio | Divide consecutive terms. | 2, 6, 18, 54 → ratio 3 |
| 3 | Check for quadratic/cubic patterns | Look at increments of increments. | 1, 4, 9, 16 → squares of 1,2,3,4 |
| 4 | Alternating pattern | Separate odd & even positions. | 2, 5, 10, 17 → 2→10→? (odd) and 5→17→? (even) |
| 5 | Special sequences | Recognize primes, Fibonacci, factorial, etc. | 2, 3, 5, 8, 13, … |
| 6 | Alphabetic shifts | Count letter positions (A=1, B=2,…). | A(1), D(4), G(7) → +3 each time |
| 7 | Pattern of operations | Note if each term is formed by +, -, ×, ÷, or a combination. | 4, 8, 12, 20 → +4, +4, +8 (next +8) |
| 8 | Look for symmetry / mirroring | Check if series forwards equals backwards. | 1, 2, 3, 2, 1 |
| 9 | Check for non‑numeric patterns | e.g., shapes, colors, directions. | (Visual series) |
Tips
- Write down the terms and compute differences/ratios in a table.
- If the series is long, try the first 3–4 terms only; patterns usually appear early.
- When stuck, try guessing a rule and test it on later terms.
- For multiple‑choice questions, eliminate obviously wrong options first.
4. Worked Example 1 – Number Series
Series:
2, 5, 10, 17, 26, …
Step 1 – Find differences
| Term | Difference from previous |
|---|---|
| 2 | – |
| 5 | 5 – 2 = 3 |
| 10 | 10 – 5 = 5 |
| 17 | 17 – 10 = 7 |
| 26 | 26 – 17 = 9 |
Step 2 – Observe the pattern in differences
Differences: 3, 5, 7, 9 → These are consecutive odd numbers increasing by 2.
Step 3 – Predict next difference
Next odd number after 9 is 11.
Step 4 – Find next term
26 + 11 = **37**
Answer: The next term is 37.
5. Worked Example 2 – Letter Series
Series:
A, D, G, J, …
Step 1 – Convert letters to positions
| Letter | Position |
|---|---|
| A | 1 |
| D | 4 |
| G | 7 |
| J | 10 |
Step 2 – Find the difference between positions
4–1 = 3
7–4 = 3
10–7 = 3
Step 3 – Apply the same difference
Next position = 10 + 3 = 13
Step 4 – Convert back to letter
13 → M
Answer: The next letter in the series is M.
6. Quick Revision Summary
- Identify the type of series (number, letter, mixed).
- Compute