Tripura TET – Reasoning Ability
Topic: Series
Series questions test your ability to spot patterns or rules in a given sequence of numbers or symbols.
Mastering series helps you solve many other reasoning problems such as numerical series, algebraic series, letter series, digit series, etc.
1. Simple Explanation
A series is a list of elements arranged in a particular order.
The task is to determine the next element (or elements) using the rule that governs the entire sequence.
Typical rules include:
| Rule | Example | Next Term |
|---|---|---|
| Arithmetic (add/subtract constant) | 2, 5, 8, 11 | 14 |
| Geometric (multiply/divide constant) | 3, 6, 12, 24 | 48 |
| Alternate addition/subtraction | 1, 4, 3, 6, 5 | 8 |
| Fibonacci‑type (sum of previous two) | 1, 1, 2, 3, 5 | 8 |
| Digit manipulation (reverse, sum of digits, etc.) | 12, 21, 33, 54 | 87 |
2. Key Points to Remember
| # | Tip | Why it matters |
|---|---|---|
| 1. Write down the series clearly | Avoid missing a term or mis‑reading a digit. | |
| 2. Check for simple arithmetic or geometric patterns first | These are the most common and quickest to spot. | |
| 3. Look for alternating patterns | Separate the even and odd positions and analyze each sub‑sequence. | |
| 4. Examine differences or ratios | Compute Δ (difference) or ÷ (ratio) between consecutive terms; constant Δ ⇒ arithmetic, constant ratio ⇒ geometric. | |
| 5. Test for sum of digits or reverse patterns | Some series involve digit manipulation (e.g., 12 → 21, 21 → 33). | |
| 6. Try Fibonacci style | The next term equals the sum of the two preceding ones. | |
| 7. Check for non‑numeric patterns | Letters, symbols, or shapes may follow alphabetical or positional rules. | |
| 8. Use elimination | If a guess leads to a contradiction, discard it. | |
| 9. Practice speed | In exam time, you’ll need to decide quickly which rule to try first. |
3. Worked Example
Series: 4, 9, 14, 19, 24, …
Step‑by‑Step Solution
| Step | Action | Result |
|---|---|---|
| 1. List the terms | 4, 9, 14, 19, 24 | |
| 2. Find differences | 9‑4 = 5, 14‑9 = 5, 19‑14 = 5, 24‑19 = 5 | |
| 3. Observe | All differences are 5 → arithmetic series with common difference +5. | |
| 4. Predict next term | 24 + 5 = 29 | |
| 5. Check | 29 fits the pattern (difference 5). |
Answer: 29
A Slightly Tricky Example
Series: 3, 6, 12, 24, 48, …
Solution
- Compute ratios:
6/3 = 2, 12/6 = 2, 24/12 = 2, 48/24 = 2 → constant ratio 2. - Next term: 48 × 2 = 96.
4. Quick Revision Summary
| Topic | Quick Point |
|---|---|
| Arithmetic Series | Constant difference Δ. Next = last + Δ. |
| Geometric Series | Constant ratio r. Next = last × r. |
| Alternating Series | Split into two sub‑series (odd & even positions). |
| Fibonacci‑type | Next = sum of previous two terms. |
| Digit Manipulation | Reverse, sum of digits, prime factors, etc. |
| Letter/Shape Series | Alphabetical order, positional value, etc. |
| General Strategy | 1) List terms. 2) Check Δ or ratio. 3) Try alternation, digit tricks, Fibonacci. 4) Validate. |
Tip: Keep a mental checklist of these five pattern types; try them in order for every series question.
Final Thought
Series questions are all about pattern recognition.
By systematically applying the above checks, you can solve most series problems efficiently and accurately—exactly what the Tripura TET exam requires. Happy practicing!