📚 Study Notes – Series (Reasoning Ability)
Program: Rajasthan Forest Guard
Subject: Reasoning Ability
Topic: Series
These notes give you a quick, clear, and practical guide to understanding and solving series questions in the RFG exam or any competitive test.
1️⃣ Simple Explanation
A series is a sequence of numbers, letters, shapes, or even words that follow a hidden rule.
When you’re asked to find the next term, missing term, or general pattern, you must identify that rule.
Key Idea:
The rule can involve arithmetic operations, geometric progressions, alternation, factorials, prime numbers, letter positions, or even a combination of several patterns.
2️⃣ Key Points & Common Patterns
| Pattern | What to Look For | Typical Formula / Example |
|---|---|---|
| Arithmetic Progression (AP) | Constant difference | a, a+d, a+2d, … |
| Geometric Progression (GP) | Constant ratio | a, ar, ar², … |
| Alternating Series | Two (or more) interleaved patterns | a, b, a+2, b+2, … |
| Reversing / Mirror | Sequence goes up then down | 1, 2, 3, 2, 1 |
| Sum of Digits / Product of Digits | Each term derived from digits of previous | 12 → 1+2=3 |
| Prime / Fibonacci / Square / Cube | Terms belong to a known sequence | 2, 3, 5, 7, 11… |
| Letter Series | Alphabet positions, skip letters | A, C, F, J… |
| Combining Rules | Two operations in one series | a + 3, a × 2, a + 3, a × 2… |
| Skipping Pattern | Every nth term follows a rule | a, a+1, a+2, a+1, a+2… |
| Cumulative Pattern | Each term is sum of all previous terms | 1, 1, 2, 4, 8… |
How to Identify the Rule
-
Check differences between consecutive terms.
- If differences are constant → AP.
- If differences themselves form a pattern → deeper rule.
-
Check ratios (divide successive terms).
- Constant ratio → GP.
-
Look for alternation:
- Split the series into even / odd positions and analyze separately.
-
Check for digit manipulation:
- Sum, product, or rearrangement of digits.
-
Test common mathematical sequences:
- Fibonacci, squares, cubes, primes.
-
Use the “test‑and‑cross” method:
- Assume a rule, compute a few terms, see if it matches given ones.
3️⃣ Worked Example
Question:
Find the next number in the series:
2, 6, 18, 54, ?
Step‑by‑Step
| Step | What to Do | Result |
|---|---|---|
| 1 | Check differences | 6-2=4, 18-6=12, 54-18=36 → differences are 4, 12, 36 (not constant). |
| 2 | Check ratios | 6/2=3, 18/6=3, 54/18=3 → constant ratio of 3. |
| 3 | Recognize GP | Common ratio r = 3. |
| 4 | Compute next term | 54 × 3 = 162. |
Answer: 162
Quick Verification
- 2 → ×3 → 6
- 6 → ×3 → 18
- 18 → ×3 → 54
- 54 → ×3 → 162
4️⃣ Quick Revision Summary
| Topic | What to remember | Quick Tips |
|---|---|---|
| Identify AP | Constant difference | d = a₂ - a₁ |
| Identify GP | Constant ratio | r = a₂ / a₁ |
| Alternation | Split series | Solve sub‑series separately |
| Digit Rules | Sum/ product of digits | Test each digit operation |
| Prime / Fibonacci | Known sequences | Memorize first 10 terms |
| Letter Series | Alphabet positions | A=1, B=2 … |
| Combining Rules | Two operations | Look for pattern changes every 2 or 3 terms |
| Check Both Directions | Ascending/Descending | Sometimes series goes up then down |
Practice Checklist
- Write the series.
- Compute first differences and ratios.
- Split into even & odd indices.
- Test digit‑based operations.
- Compare with known sequences.
- Confirm with a few more terms.
Final Tips
- Time Management: Allocate 1–2 minutes per series question.
- Eliminate Impossible Patterns: If a rule leads to a non‑integer or negative number when the series is all positive integers, discard it.
- Always Verify: After finding a rule, check it against every given term before finalizing the answer.
Good luck with your RFG preparation! 🚀