Reasoning Ability – Series
(Odisha Police Constable Exam – Beginner Notes)
1. What is a “Series”?
A series is a list of numbers that follows a hidden rule.
Think of it like a recipe where every step depends on the previous one.
Everyday analogy:
Imagine you’re watering plants.
You water 1 cup today, 2 cups tomorrow, 4 cups the next day, and so on.
The amount of water each day follows a rule – that’s a series.
2. Why Do We Use Series in Exams?
- To test your pattern‑recognition skills.
- Helps you solve problems quickly once you see the rule.
- Common in reasoning tests, aptitude sections, and police exams.
3. Common Types of Series
| Type | Typical Rule | Everyday Analogy |
|---|---|---|
| Arithmetic | Add/subtract the same number each step. | Adding 5 candies after each round. |
| Geometric | Multiply/divide by the same number each step. | Doubling a money amount every month. |
| Fibonacci | Add the last two numbers to get the next. | Growing rabbit pairs: 1, 1, 2, 3, 5, 8… |
| Alternating | Two (or more) rules switch back and forth. | Odd days you add 3, even days you subtract 2. |
| Square/Cube | Numbers are perfect squares or cubes. | 1², 2², 3² … or 1³, 2³, 3³. |
| Prime/Composite | Only prime or composite numbers. | 2, 3, 5, 7, 11… |
| Miscellaneous | Patterns like 1, 4, 9, 16 (squares), 2, 6, 12 (multiples of 6), etc. | Counting steps in a staircase. |
4. How to Spot the Rule – Step‑by‑Step
-
Write the series down clearly.
Example: 3, 7, 11, 15, … -
Check differences between consecutive terms.
7‑3 = 4, 11‑7 = 4, 15‑11 = 4 → Constant difference → Arithmetic. -
If differences are not constant, check ratios (multiplication).
Example: 2, 6, 18, 54 → 6/2 = 3, 18/6 = 3, 54/18 = 3 → Constant ratio → Geometric. -
If neither difference nor ratio is constant, look for other patterns:
- Sum of previous two numbers? (Fibonacci)
- Alternating add/subtract?
- Powers of 2, 3, …
- Prime numbers?
- Squares/cubes?
- Any other “nice” simple rule.
-
Verify by checking the next term(s).
If the rule holds for all given terms, you’re likely correct.
5. Tiny Examples
Example 1 – Arithmetic Series
Series: 4, 9, 14, 19, …
Step:
- 9‑4 = 5, 14‑9 = 5, 19‑14 = 5 → Constant difference = 5.
Rule: Add 5 each time.
Next term: 19 + 5 = 24.
Example 2 – Geometric Series
Series: 3, 9, 27, 81, …
Step:
- 9/3 = 3, 27/9 = 3, 81/27 = 3 → Constant ratio = 3.
Rule: Multiply by 3 each time.
Next term: 81 × 3 = 243.
Example 3 – Alternating Series
Series: 1, 4, 2, 5, 3, 6, …
Step:
- Notice two separate patterns:
- Odd positions: 1, 2, 3 → +1 each step.
- Even positions: 4, 5, 6 → +1 each step.
Rule: Increase alternately.
Next term (position 7, odd): 3 + 1 = 4.
Example 4 – Fibonacci‑style
Series: 2, 3, 5, 8, 13, …
Rule: Each number = sum of the two before it.
Next term: 8 + 13 = 21.
6. Quick Tips for Exam Time
| Tip | Why It Helps |
|---|---|
| Skip the long ones – If a series is 8+ numbers, find a quick rule on the first 3–4. | |
| Look for “nice” numbers – 0, 1, 2, 4, 5, 10, 12, 15, 20 are common. | |
| Check if the series is “backwards” – Sometimes they give the last few terms. | |
| Use the “difference of squares” trick – For 1, 4, 9, 16… difference grows by 2 each time. | |
| Practice with 5–10 sample series – Builds pattern‑recognition muscle. |
7. Mini Practice Problems
-
Series: 5, 10, 20, 40, … → What is the next number?
Hint: Look at ratio. -
Series: 10, 7, 4, 1, … → Next?
Hint: Subtract 3 each time. -
Series: 1, 4, 9, 16, 25, … → What comes next?
Hint: These are perfect squares. -
Series: 2, 4, 8, 16, 32, … → Next?
Hint: Multiply by 2 each time. -
Series: 1, 3, 2, 4, 3, 5, … → Find the 7th term.
Hint: Two interleaved sequences.
*(Try to solve before pe