Series: Reasoning Ability Notes for Meghalaya Police Constable

📚 Reasoning Ability – Series

Target Exam: Meghalaya Police Constable
Topic: Series

Series problems are one of the most common items in reasoning sections.
They test pattern recognition, logical deduction, arithmetic skills, and the ability to spot hidden rules.
Mastering series gives you a solid edge in any reasoning paper.

1️⃣ Simple Explanation

A series is a sequence of numbers written in a particular order.

Pattern: The rule that generates the next element(s).
Goal: Identify the rule and predict the next term(s).

Common patterns:

Pattern	Example	Rule
Arithmetic	2, 5, 8, 11	+3 each step
Geometric	3, 9, 27	×3 each step
Fibonacci	1, 1, 2, 3, 5	Sum of last two
Alternating	4, 9, 2, 7	+5, –7, +5, –7
Prime‑based	2, 3, 5, 7	Next prime
Position‑based	1, 4, 9, 16	(n^2)

Tip: Look for the smallest change (difference, ratio, pattern in digits, etc.) first.

2️⃣ Key Points to Remember

#	Key Point	Why it matters
1	Start with the first two terms.	They usually give the simplest hint (difference, ratio, or operation).
2	Check both difference and ratio.	Many series are arithmetic or geometric.
3	Look for alternating patterns.	Odd‑even positions might follow separate rules.
4	Consider digit patterns.	Series may involve reversing, adding digits, or manipulating digits.
5	Prime/Composite check.	Some series use primes, factorials, or squares/cubes.
6	Position‑based formulas.	Terms may equal (n^2, n^3, n!), etc.
7	Skip terms if needed.	Sometimes the rule applies every 2nd or 3rd term.
8	Verify with multiple terms.	A guessed rule must work for all given numbers.
9	Time management.	If stuck, move on and return if time allows.
10	Practice with past exam patterns.	Meghalaya Police Constable papers often use simple arithmetic/geometric series.

3️⃣ Worked Example

Question:
Find the next number in the series:

4, 9, 14, 19, 24, ?

Step‑by‑Step Solution

Calculate differences between consecutive terms:
- 9 – 4 = 5
- 14 – 9 = 5
- 19 – 14 = 5
- 24 – 19 = 5
The difference is constant (+5).
Identify the rule:
This is an Arithmetic Series with common difference d = 5.
Predict the next term:
Next term = Last term + d = 24 + 5 = 29.
Check:
29 – 24 = 5 → rule holds.

Answer: 29

Another Example (Mixed Pattern)

Series: 2, 6, 10, 17, 23, ?

Look at differences:
- 6 – 2 = 4
- 10 – 6 = 4
- 17 – 10 = 7
- 23 – 17 = 6
Differences: 4, 4, 7, 6 → not constant.
Check alternating pattern:
- Odd positions: 2, 10, 23 → differences 8, 13
- Even positions: 6, 17 → difference 11
Not consistent.
Try position‑based formula:
- Observe: 2 = 1² + 1, 6 = 2² + 2, 10 = 3² + 1, 17 = 4² + 1, 23 = 5² + 2
  Not clear.
Alternative approach – sum of digits or prime addition?
- 2 (prime), 6 (prime+1), 10 (prime+3), 17 (prime+4), 23 (prime+?).
Check if rule is “add successive prime numbers”:
- Primes: 2, 3, 5, 7, 11
- 2 + 2 = 4 (not 6).
- 2 + 3 = 5 (not 6).
Try “add increasing numbers 4,4,7,6”
Sequence of added numbers: 4,4,7,6.
Next added number might follow pattern 4,4,7,6,? → maybe 7 again?
Compute next term if add 7:
23 + 7 = 30.
Check if 30 fits some hidden rule?
Not obvious.

Result: This series is ambiguous without more context.
Lesson: Sometimes the pattern is not obvious; skip if time‑constrained.

4️⃣ Quick Revision Summary

Stage	What to Do	Quick Check
1. Examine first two terms	Compute difference & ratio	Both simple → likely arithmetic/geometric
2. Look for constant difference/ratio	Add or multiply accordingly	Works for all terms?
3. Check alternating pattern	Separate odd/even terms	Do they each follow a rule?
4. Inspect digit manipulation	Reverse, add digits, etc.	Does pattern repeat every 2–3 terms?
5. Test position‑based formulas	(n^2