Study Notes – Reasoning Ability
Topic: Series
(For Lakshadweep TET – Teacher Eligibility Test)
1. Simple Explanation
A series is a sequence of numbers arranged in a specific order where each number follows a rule or pattern. In reasoning tests, you’ll be asked to:
- Identify the missing term(s).
- Predict the next term(s).
- Find the rule generating the series.
Common series types:
| Type | Example | Rule |
|---|---|---|
| Arithmetic (A.P.) | 3, 7, 11, 15 | Common difference = +4 |
| Geometric (G.P.) | 2, 6, 18, 54 | Common ratio = ×3 |
| Fibonacci / Fibonacci‑like | 1, 1, 2, 3, 5, 8 | Next = sum of previous two |
| Square / Cube | 1, 4, 9, 16 | n² |
| Factorial | 1, 2, 6, 24 | n! |
| Prime Numbers | 2, 3, 5, 7 | Next prime |
| Skipping / Interleaved | 5, 2, 9, 6, 13 | Two interleaved A.P.’s |
| Pattern in digits | 12, 21, 13, 31 | Reverse digits, add 1, etc. |
2. Key Points to Remember
| # | Point | Why It Matters |
|---|---|---|
| 1 | Identify the type first – Look for constant difference → A.P.; constant ratio → G.P.; sum pattern → Fibonacci; squares/cubes → powers. | Saves time and avoids guessing. |
| 2 | Check for two interleaved series – If the series alternates in a way that two different patterns appear, split into two subsequences. | Common trick in TET questions. |
| 3 | Look for operations on digits – Sometimes the rule is on the digits (e.g., reverse, add 1, multiply digits). | Helps when numeric patterns don’t fit A.P./G.P. |
| 4 | Use “difference of squares” or “difference of cubes” – If the increase between terms grows rapidly, consider squares/cubes. | Recognizes series like 1, 4, 9, 16 … |
| 5 | Check for factorial or prime patterns – These series grow quickly; if numbers jump sharply, consider n! or primes. | Avoids misidentifying a fast‑growing series as G.P. |
| 6 | Remember “skip” patterns – Series may skip numbers (e.g., 1, 4, 7, 10 → add 3 each time). | A simple A.P. with a different common difference. |
| 7 | Validate with two terms – Once you think you’ve found a rule, verify it with at least two more terms. | Prevents accidental coincidence. |
| 8 | Use “sum of digits” or “product of digits” – Some series are defined by digit operations. | Useful for digit‑based patterns. |
| 9 | Keep track of negative or zero values – Sometimes series include negatives or zeros. | Adjust the rule accordingly. |
| 10 | Practice with time limits – TET has a 30‑minute reasoning section. | Speed improves accuracy. |
3. Worked Example
Question
Find the missing number in the series:
4, 12, 28, 64, __?
A. 128
B. 120
C. 140
D. 96
Solution
-
Look for a pattern
Differences:- 12 – 4 = 8
- 28 – 12 = 16
- 64 – 28 = 36
The differences themselves are: 8, 16, 36.
Notice: 8 = 2² × 2, 16 = 4², 36 = 6². -
Pattern of differences
The differences increase as squares of even numbers:- 2² = 4 → ×2 = 8
- 4² = 16
- 6² = 36
So the next difference should be 8² = 64.
-
Find next term
64 (last given term) + 64 (next difference) = 128.
Answer: A. 128
4. Quick Revision Summary
| Item | Reminder |
|---|---|
| Identify series type – A.P., G.P., Fibonacci, squares, factorial, primes, digit patterns. | |
| Split into two interleaved series if pattern alternates. | |
| Check differences or ratios – constant difference → A.P.; constant ratio → G.P. | |
| Look for digit operations – reverse, add/subtract, multiply digits. | |
| Validate with at least two terms after guessing a rule. | |
| Practice – solve 5–10 series problems a day, time yourself. | |
| Common traps – assuming G.P. when difference grows, ignoring digit patterns. |
Final Tip
During the exam, first scan the series for any obvious arithmetic or geometric patterns. If nothing fits, try splitting the series or looking for digit‑based rules. Keep a notebook of the most common patterns for quick reference. Good luck!