📚 Reasoning Ability – Series
Program: Jammu & Kashmir Police Sub‑Inspector (SI)
Target: Quick, clear, and practical study notes for exam preparation
1️⃣ Simple Explanation
A series is a set of numbers arranged in a specific order, usually following a rule or pattern.
When you are asked to find the next term, missing term, or sum of terms, you need to:
- Recognise the type of series (Arithmetic, Geometric, Fibonacci, Harmonic, etc.).
- Determine the rule that generates each term.
- Apply the rule to the given data to solve the problem.
2️⃣ Key Points – Types of Series & How to Spot Them
| Type | Definition | Common Pattern | Quick Identifiers |
|---|---|---|---|
| Arithmetic Series (AP) | Each term = previous term + constant difference (d) | a, a+d, a+2d, … |
Constant difference, linear graph |
| Geometric Series (GP) | Each term = previous term × common ratio (r) | a, ar, ar², … |
Ratio of consecutive terms ≈ constant |
| Fibonacci/Successive Sum Series | Each term = sum of two preceding terms | a, b, a+b, b+(a+b), … |
Each term roughly doubles the previous |
| Harmonic Series | Each term = 1 / (integer) | 1, 1/2, 1/3, … |
Terms are fractions of decreasing denominators |
| Alternating Series | Sign or pattern alternates | a, -b, a, -b … |
Alternating sign or magnitude |
| Mixed Series | Combination of two or more patterns | 1, 2, 3, 6, 7, 8, 16… |
Look for repeated sub‑patterns |
Quick Checklist to Identify
- Check differences – if constant → AP.
- Check ratios – if constant → GP.
- Check previous two terms – if sum → Fibonacci.
- Check reciprocals – if they form AP → Harmonic.
- Look for sign alternation – → Alternating.
- If none fit, look for a two‑term or four‑term repeating pattern.
3️⃣ Worked Example
Problem
The series is:
2, 6, 18, 54, ?
Find the missing term.
Step‑by‑step
- Notice the ratio between consecutive terms:
- 6 ÷ 2 = 3
- 18 ÷ 6 = 3
- 54 ÷ 18 = 3
The ratio is constant (3).
- Identify as a Geometric Series (GP) with first term
a = 2and common ratior = 3. - Find the next term:
54 × 3 = 162. - Answer:
162.
Extra Check
- General term formula for GP:
Tₙ = a·rⁿ⁻¹.
Forn = 5:T₅ = 2·3⁴ = 2·81 = 162. ✔️
4️⃣ Quick Revision Summary
| Point | What to Review |
|---|---|
| Definition of series | Sequence of numbers generated by a rule |
| Types | AP, GP, Fibonacci, Harmonic, Alternating, Mixed |
| Identification tricks | Differences, ratios, sums of two terms, reciprocals |
| Formulas | AP: Tₙ = a + (n-1)d GP: Tₙ = a·rⁿ⁻¹ Sum AP: Sₙ = n/2 (2a + (n-1)d) Sum GP: Sₙ = a (1 - rⁿ)/(1 - r) |
| Common pitfalls | Confusing AP/GP when ratio ≈ difference; forgetting to check sign alternation; mis‑applying Fibonacci rule |
| Practice tips | Solve 5‑6 problems from each type daily; create a quick reference chart; time yourself on exam‑style questions |
Final Thought
Mastering series in reasoning ability is all about pattern recognition.
Use the quick checklist to instantly classify any series, then apply the appropriate rule.
Practice regularly, and you’ll tackle series questions with confidence and speed. Good luck, future Sub‑Inspector! 🚓✨