Series – Reasoning Ability
(For LIC / GIC Exam Preparation)
1. Simple Explanation
In a series you are given a sequence of numbers (or letters, shapes, etc.) and you must identify the rule that governs the sequence. Once the rule is known, you can predict the next element(s) or fill in missing blanks.
Typical series types:
| Type | Definition | Example |
|---|---|---|
| Arithmetic | Each term differs from the previous by a constant difference | 2, 5, 8, 11, … (difference = +3) |
| Geometric | Each term is multiplied/divided by a constant ratio | 3, 6, 12, 24, … (ratio = ×2) |
| Fibonacci (Recursive) | Each term is the sum of the two preceding terms | 1, 1, 2, 3, 5, 8, … |
| Alternating Series | Two (or more) patterns alternate | 4, 9, 16, 25, … (squares of 2,3,4,5…) |
| Digit/Factorial Patterns | Use of digits, factorials, primes, etc. | 1, 2, 6, 24, 120 … (n!) |
| Complex/Composite | Combination of the above or other operations | 2, 4, 8, 12, 20, 24, … (add 2, add 4, add 8, add 12…) |
2. Key Points to Remember
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Look for Simple Operations First
- Add/Subtract → Arithmetic
- Multiply/Divide → Geometric
- Sum of previous two → Fibonacci
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Check for Alternating Patterns
- Group terms by position (odd/even) and see if each group follows its own rule.
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Examine Digits or Factors
- Prime numbers, squares, cubes, factorials, or digit sums can form the rule.
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Multiple Operations
- Some series combine operations (e.g., add 2, multiply 3, subtract 1, add 4…).
- Identify the cycle length (how many terms before the pattern repeats).
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Use the Given Terms
- Compute differences or ratios between consecutive terms; they often reveal the rule.
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When in Doubt, Test Hypotheses
- Apply a potential rule to see if it fits all given terms.
- If it fails, backtrack and try another.
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Practice Speed
- For exam time, practice spotting the pattern in the first 2–3 terms; the rest usually follows.
3. Worked Example
Series:
5, 12, 23, 38, 57, …
Step 1 – Compute Differences
- 12 – 5 = 7
- 23 – 12 = 11
- 38 – 23 = 15
- 57 – 38 = 19
Step 2 – Examine the Differences
The differences themselves form a pattern:
7, 11, 15, 19 – they increase by 4 each time.
Step 3 – Predict the Next Difference
Next difference = 19 + 4 = 23
Step 4 – Find the Next Term
57 + 23 = 80
Answer: The next number in the series is 80.
Rule:
- Start with 5.
- Add 7, then add 11, then 15, then 19, …
- The added number is
4n + 3wherenstarts at 1 (i.e., 7 = 4×1+3, 11 = 4×2+3, …).
4. Quick Revision Summary
| Feature | What to Look For | Typical Operation |
|---|---|---|
| Arithmetic | Constant difference | + / – |
| Geometric | Constant ratio | × / ÷ |
| Fibonacci | Sum of last two | + (recursive) |
| Alternating | Two patterns interleave | +, – or ×, ÷ alternating |
| Digits/Factors | Prime, square, factorial | +, ×, digit sum |
| Composite Pattern | Cycle of operations | Mixed (+, ×, –) |
Tips for LIC/GIC Exams
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Time‑saving trick: Write the first 4–5 terms, compute differences/ratios, and see if a simple arithmetic/ geometric rule emerges.
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Common exam patterns:
- Squares of consecutive integers
- Double, then add 1 (or subtract 1)
- Prime numbers in sequence
- Cyclic patterns of length 3 or 4
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Practice problem to try:
3, 11, 23, 39, 59, …
(Answer: 83 – difference increases by 8 each time.)
Final Thought
Mastering series comes down to pattern recognition. By systematically checking differences, ratios, and possible alternating or composite rules, you can quickly uncover the hidden logic and answer any series question confidently on the exam. Happy practicing!