Maharashtra PSC – Reasoning Ability
Topic: Series
Series problems test your ability to spot hidden patterns and extrapolate the next element(s).
In exams you’ll encounter arithmetic, geometric, harmonic, Fibonacci‑type, and mixed series.
1. Simple Explanation
A series is a sequence of numbers written in a specific order.
To solve a series question, you must:
- Look for a consistent rule that transforms one term into the next.
- Test common patterns (add/subtract, multiply/divide, alternating operations, squares/cubes, etc.).
- Apply the rule to find the missing term(s).
2. Key Points / Checklist
| Pattern | How to Spot It | Typical Operations | Example |
|---|---|---|---|
| Arithmetic Series | Constant difference between successive terms | + / – | 3, 7, 11, 15, … (diff = +4) |
| Geometric Series | Constant ratio between successive terms | × / ÷ | 2, 6, 18, 54, … (ratio = ×3) |
| Harmonic Series | Reciprocal of an arithmetic series | 1/n | 1, 1/2, 1/3, 1/4, … |
| Fibonacci‑type | Sum of previous one or two terms | + | 1, 1, 2, 3, 5, 8, … |
| Alternating Operations | Different operations on odd/even positions | +, – on odd; ×, ÷ on even | 2, 4, 3, 9, 6, 18, … |
| Squares / Cubes | Terms are perfect powers | n², n³ | 1, 4, 9, 16, … |
| Mixed | Combination of two or more rules | – | 2, 4, 8, 7, 14, 13, 26, … (×2, –1) |
Quick Tips
- Check first 3–4 terms; if they fit a rule, try confirming with the next term.
- Look for patterns in digits (e.g., 12, 24, 48 – double each time).
- If no simple rule appears, test the difference of differences or ratio of differences (helps with quadratic patterns).
- Beware of traps: sometimes a series uses a rule that changes after a few terms (e.g., +5, –3, +5, –3…).
3. Worked Example
Question
Find the missing term in the series:
5, 11, 23, 47, ?, 191
Step‑by‑Step
-
Find the differences between successive terms:
- 11 – 5 = 6
- 23 – 11 = 12
- 47 – 23 = 24
- ? – 47 = ?
- 191 – ? = ?
The differences look like: 6, 12, 24, … → each double the previous.
-
Predict the next difference:
24 × 2 = 48
So, the missing term = 47 + 48 = 95. -
Check the last difference:
191 – 95 = 96, which is indeed 48 × 2 (continuing the doubling pattern).
Hence the series is consistent.
Answer: The missing term is 95.
4. Quick Revision Summary
| Item | What to Remember |
|---|---|
| Identify the pattern | Arithmetic, geometric, harmonic, Fibonacci, alternating, powers, or mixed. |
| Use differences/ratios | Helps spot arithmetic or geometric series. |
| Check the first 3–4 terms | If they fit a rule, test the next one. |
| Watch for digit patterns | e.g., doubling digits, adding/subtracting a fixed number. |
| Beware of mixed rules | Remember to re‑check after a few terms. |
| Practice | Solve at least 10 series problems daily; time yourself. |
Tip for Maharashtra PSC: In multiple‑choice questions, if two options fit the pattern, check the next term in the series. The correct option will keep the pattern consistent beyond the missing value.
Happy studying!