📚 Reasoning Ability – Series
Course: LIC AAO (Life Insurance Corporation – Associate of Accounting Officer)
Topic: Series
Audience: Exam‑preparation candidates
Series are sequences that follow a hidden rule.
Identifying the rule is the key to predicting the next element(s).
1. Simple Explanation
A series is a list of numbers, letters, or words arranged in a specific order.
The order is governed by a pattern (addition, multiplication, alternation, etc.).
Your job is to spot the pattern and use it to find the missing term(s) or the next term(s).
2. Key Points & Techniques
| Pattern Type | Common Examples | How to Spot It | Formula / Trick |
|---|---|---|---|
| Arithmetic Progression (AP) | 3, 7, 11, 15 … | Constant difference (d) | a_n = a_1 + (n-1)d |
| Geometric Progression (GP) | 2, 4, 8, 16 … | Constant ratio (r) | a_n = a_1 * r^(n-1) |
| Fibonacci / Cumulative | 1, 1, 2, 3, 5, 8 … | Each term = sum of previous two | a_n = a_{n-1} + a_{n-2} |
| Alternating / Group Patterns | 4, 9, 4, 9, … | Two or more sub‑patterns repeating | Identify sub‑sequence |
| Difference / Ratio Tables | 2, 5, 10, 17 … | Build table of differences | Look for constant or pattern |
| Alphabetic / Letter Series | A, D, G, J … | Step in alphabet | next = prev + step |
| Word Series (Synonyms, Antonyms) | Cat, Dog, Mouse … | Semantic relation | Understand category |
| Prime / Composite Patterns | 2, 3, 5, 7, 11 … | Prime numbers | Use primality test |
| Square / Cube / Factorial | 1, 4, 9, 16 … | Squares | n^2 |
| Special Sequences | 1, 3, 6, 10, 15 … (triangular) | n(n+1)/2 |
Recognize shape |
General Steps to Solve
- Write down the series clearly.
- Check simple arithmetic: differences, ratios.
- Look for repeating groups (two‑term, three‑term, etc.).
- Try cumulative patterns (sum of previous terms).
- If numbers, try squares / cubes / factorials.
- If letters/words, consider alphabetic or semantic rules.
- Validate your rule by applying it to all given terms.
- Predict the missing/next term.
Common Pitfalls
| Mistake | Why it Happens | Fix |
|---|---|---|
| Assuming a pattern too early | Early terms fit many rules | Verify with later terms |
| Ignoring negative or zero values | They change difference/ratio | Include them in calculations |
| Missing alternating patterns | Sub‑patterns overlap | Separate into sub‑series |
| Over‑complicating | Too many operations | Start with simplest (AP/GP) |
3. Worked Example
Example 1 – Number Series
Series: 2, 6, 12, 20, 30, ?
Step‑by‑Step
| Term | 1 | 2 | 3 | 4 | 5 | 6 |
|---|---|---|---|---|---|---|
| Value | 2 | 6 | 12 | 20 | 30 | ? |
| Difference | - | +4 | +6 | +8 | +10 | ? |
- Differences: 4, 6, 8, 10 → increasing by 2 each time.
- Next difference = 10 + 2 = 12.
- Next term = 30 + 12 = 42.
Answer: 42
Example 2 – Letter Series
Series: A, D, G, J, ?
Step‑by‑Step
- Alphabet positions: A=1, D=4, G=7, J=10
- Each step increases by 3.
- Next position = 10 + 3 = 13 → letter M.
Answer: M
Example 3 – Word Series (Synonyms)
Series: Small, Little, Tiny, ?
Step‑by‑Step
- All words mean “very small”.
- Next word with same meaning: **Miniature