Series – Reasoning Ability Study Notes
(Assam PSC – Reasoning Ability – Series)
1. What is a “Series”?
A series is a list of numbers, letters, shapes or any objects arranged in a specific order.
The next item (or missing items) is determined by a hidden rule – arithmetic, geometric, pattern in digits, alternating sub‑series, etc.
Goal of the question – identify the rule and apply it to find the missing term(s) or the next term.
2. Types of Series & Common Patterns
| Type | Example | Rule / Observation | Typical Method |
|---|---|---|---|
| Arithmetic (A.P.) | 3, 7, 11, 15 | Constant difference (+4) | Find common difference |
| Geometric (G.P.) | 2, 6, 18, 54 | Constant ratio (×3) | Find common ratio |
| Square Numbers | 1, 4, 9, 16 | n² | Find n |
| Cube Numbers | 8, 27, 64 | n³ | Find n |
| Prime Numbers | 2, 3, 5, 7 | Prime sequence | Recognise primes |
| Fibonacci / Recurrence | 1, 1, 2, 3, 5 | Sum of previous two | Add previous two |
| Alternating Sub‑Series | 1, 4, 2, 5, 3, 6 | Two interleaved patterns | Separate into two series |
| Digit Patterns | 12, 21, 33, 54 | Reverse digits, or sum of digits | Look at digits individually |
| Letter Series | A, D, G, J | +3 letters each step | Convert to alphabet index |
| Mixed Operations | 2, 5, 10, 17 | +3, +5, +7 (odd numbers) | Identify operation pattern |
Tip: If the series is not immediately obvious, try the difference (Δ) and ratio (÷) tables first. If they are not constant, look for alternating patterns or digit‑wise rules.
3. Step‑by‑Step Strategy
| Step | What to Do | Why |
|---|---|---|
| 1. Write the series clearly | List each term on a new line or in a table | Visual clarity helps spotting patterns |
| 2. Check Δ (difference) | Subtract successive terms | Reveals arithmetic or mixed differences |
| 3. Check ÷ (ratio) | Divide successive terms | Reveals geometric or mixed ratios |
| 4. Look at digits / letters | Split digits, reverse, sum, look for alphabets | Many questions use digit tricks |
| 5. Consider sub‑series | Split even/odd positions or groups | Alternating patterns are common |
| 6. Test a few hypotheses | Try arithmetic, geometric, squares, etc. | Narrow down possibilities quickly |
| 7. Verify with all terms | Confirm the rule fits every term | Avoids guessing |
| 8. Find the missing term | Apply the rule to the position in question | Final answer |
4. Worked Example
Question
Find the missing number in the series:
4, 9, 16, 25, ___
Step‑by‑Step
| Step | Action | Observation |
|---|---|---|
| 1. List | 4, 9, 16, 25 | |
| 2. Δ | 5, 7, 9 | Δ is not constant → not simple A.P. |
| 3. Check pattern | 4 = 2², 9 = 3², 16 = 4², 25 = 5² | Squares of consecutive integers |
| 4. Next term | 6² = 36 | |
| Answer | 36 |
Quick Recap
- Notice the square pattern.
- Each term is n² where n = 2, 3, 4, 5, …
- Next n = 6 → 6² = 36.
5. Practice Question (Try Yourself)
7, 12, 19, 28, ___
Hint: Look at the differences → 5, 7, 9 (odd numbers increasing by 2).
Add 11 to 28 → 39.
6. Quick Revision Checklist
| ✔️ | Question |
|---|---|
| 1. Can I write the series in a table? | |
| 2. What is Δ (difference) between successive terms? | |
| 3. |