Logical and Abstract Reasoning assesses a candidate’s ability to think critically, detect patterns, interpret relationships, and solve problems systematically. In emergency services like the Ghana National Fire Service (GNFS), officers must make rapid decisions under pressure. This module strengthens mental agility and structured thinking.

UNIT 1: Number Sequences

Concept Explanation

A number sequence is a series of numbers arranged according to a specific rule or pattern. The candidate must determine the pattern and predict the next number(s).

Common Types of Number Sequences

Type	Description	Formula / Rule	Example
Arithmetic Sequence	Constant difference between terms	Tₙ = a + (n − 1)d	2, 5, 8, 11
Geometric Sequence	Constant ratio between terms	Tₙ = a(r)ⁿ⁻¹	3, 6, 12, 24
Square Numbers	Perfect squares	n²	1, 4, 9, 16
Alternating Pattern	Two interwoven sequences	Identify each separately	2, 5, 4, 7, 6, 9

1. Arithmetic Sequence

Formula:

Tₙ = a + (n − 1)d

Where:

Tₙ = nth term
a = first term
d = common difference
n = term position

Example:
Find the next number: 4, 9, 14, 19, ___
Difference = 5
Next term = 19 + 5 = 24

2. Geometric Sequence

Formula:

Tₙ = a(r)ⁿ⁻¹

Where:

r = common ratio

Example:
3, 6, 12, 24, ___
Multiply by 2
Next = 48

UNIT 2: Letter Series

Concept Explanation

Letter series follow alphabetical patterns based on position in the alphabet.

Alphabet Positions:

A=1, B=2, C=3 … Z=26

Example 1:

A, C, E, G, ___
Positions: 1, 3, 5, 7
Add 2 each time
Answer: I (9)

Example 2 (Alternating Pattern):

B, E, D, G, F, ___
Pattern 1: B, D, F
Pattern 2: E, G, ___
Second pattern adds 2 → I

Teaching Tip:

Convert letters to numbers before solving.

UNIT 3: Pattern Recognition

Concept Explanation

Pattern recognition involves identifying visual or symbolic changes in shapes, diagrams, or symbols.

Common Changes:

Pattern Type	Description
Rotation	Shape turns 90°, 180°
Reflection	Mirror image
Shading	Increase or decrease shading
Movement	Object shifts position

Example:

If a triangle rotates 90° clockwise each step, predict the next orientation.

Students should:

Identify direction of movement.
Observe changes in position.
Count number of elements added/removed.

UNIT 4: Analogies

Concept Explanation

Analogies test relationship reasoning.

Format:

A : B :: C : ?

Means: A is related to B in the same way C is related to ?

Types of Analogies

Type	Example	Explanation
Function	Knife : Cut :: Pen : Write	Tool and function
Part to Whole	Wheel : Car :: Finger : Hand	Component relationship
Cause & Effect	Fire : Smoke :: Rain : Flood	Result relationship
Degree	Warm : Hot :: Cold : Freezing	Intensity progression

Solving Strategy

Identify relationship between first pair.
Apply same logic to second pair.
Eliminate wrong options.

UNIT 5: Deductive Reasoning

Concept Explanation

Deductive reasoning involves drawing specific conclusions from general statements.

Structure:

Premise 1
Premise 2
Conclusion

Example:

Premise 1: All firefighters wear uniforms.
Premise 2: Kwame is a firefighter.
Conclusion: Kwame wears a uniform.

This is logically valid.

Common Logical Forms

Type	Structure	Example
Modus Ponens	If P → Q	If fire occurs, alarm sounds
Modus Tollens	If P → Q, not Q → not P	If alarm not sound, no fire

UNIT 6: Logical Problem Solving

Concept Explanation

Requires structured thinking and elimination.

Example:

Three firefighters A, B, C respond to calls on different days.
Clues are given.
Students must deduce correct arrangement.

Teaching Approach

List all possibilities.
Use elimination method.
Create tables if needed.

Example Table:

Officer	Monday	Tuesday	Wednesday
A	✔
B		✔
C			✔

Importance for Fire Service

In real emergencies, officers must:

Analyze information quickly
Identify patterns
Make correct decisions under pressure

(Worked Examples and Structured Solutions)

UNIT 1: Number Sequences

1.1 Arithmetic Sequences

Definition

An arithmetic sequence is a sequence where the difference between consecutive terms is constant.

Formula

Tₙ = a + (n − 1)d

Where:
Tₙ = nth term
a = first term
d = common difference
n = term number

Worked Example 1

Find the 10th term of the sequence:

3, 7, 11, 15, …

Step 1: Identify first term
a = 3

Step 2: Find common difference
7 − 3 = 4
11 − 7 = 4
d = 4

Step 3: Apply formula

Tₙ = a + (n − 1)d
T₁₀ = 3 + (10 − 1)4
T₁₀ = 3 + (9 × 4)
T₁₀ = 3 + 36
T₁₀ = 39

Answer: 39

Worked Example 2

Find the next number:

5, 9, 13, 17, ___

Difference:

9 − 5 = 4
13 − 9 = 4
17 − 13 = 4

Next = 17 + 4 = 21

1.2 Geometric Sequences

Definition

A geometric sequence has a constant ratio between terms.

Formula

Tₙ = a(r)ⁿ⁻¹

Where:
r = common ratio

Worked Example 3

Find the 6th term:

2, 6, 18, 54, …

Step 1: Find ratio

6 ÷ 2 = 3
18 ÷ 6 = 3

r = 3

Step 2: Apply formula

T₆ = 2(3)⁶⁻¹
T₆ = 2(3)⁵
T₆ = 2(243)
T₆ = 486

Answer: 486

1.3 Alternating Sequences

Worked Example 4

Find the next term:

2, 5, 4, 7, 6, ___

Split into two sequences:

Sequence 1	2	4	6
Sequence 2	5	7	?

Sequence 1: +2
Sequence 2: +2

Next = 9

Answer: 9

UNIT 2: Letter Series

Convert letters to numbers:

A=1, B=2, C=3 ... Z=26

Worked Example 5

Find the next letter:

A, D, G, J, ___

Step 1: Convert to numbers

Letter	A	D	G	J
Number	1	4	7	10

Pattern: +3

Next number:

10 + 3 = 13

13 = M

Answer: M

Worked Example 6 (Alternating)

B, E, D, G, F, ___

Convert:

Letter	B	E	D	G	F
Number	2	5	4	7	6

Split pattern:

Sequence 1: 2, 4, 6 (+2)
Sequence 2: 5, 7, ___ (+2)

Next number = 9

9 = I

Answer: I

UNIT 3: Pattern Recognition

Types of Visual Patterns

Type	Description
Rotation	Shape turns 90° or 180°
Reflection	Mirror image
Progression	Elements increase/decrease
Movement	Object shifts position

Worked Example 7 (Rotation Concept)

If a square rotates 90° clockwise each step:

Step 1 → 0°
Step 2 → 90°
Step 3 → 180°
Step 4 → 270°

Next rotation:

270° + 90° = 360°

360° returns to original position.

Answer: Original orientation.

Worked Example 8 (Element Increase)

1 dot
2 dots
4 dots
8 dots

Pattern: multiply by 2

8 × 2 = 16

Answer: 16 dots.

UNIT 4: Analogies

Structure:

A : B :: C : ?

Means: A is related to B the same way C is related to ?

Common Relationship Types

Type	Example
Function	Knife : Cut
Part–Whole	Wheel : Car
Cause–Effect	Fire : Smoke
Degree	Warm : Hot

Worked Example 9

Fire : Smoke :: Rain : ?

Relationship: Cause → Effect

Rain causes Flood

Answer: Flood

Worked Example 10

Finger : Hand :: Leaf : ?

Relationship: Part to Whole

Leaf is part of Tree

Answer: Tree

UNIT 5: Deductive Reasoning

Structure:

Premise 1
Premise 2
Conclusion

Logical Forms

Modus Ponens

If P → Q
P is true
Therefore Q is true

Worked Example 11

Premise 1: If there is fire, smoke is present.
Premise 2: There is fire.

Conclusion:

Smoke is present.

Modus Tollens

If P → Q
Q is false
Therefore P is false

Worked Example 12

Premise 1: If alarm rings, there is danger.
Premise 2: There is no danger.

Conclusion:

Alarm did not ring.

UNIT 6: Logical Problem Solving

Strategy

List possibilities
Eliminate impossible options
Use table format

Worked Example 13

Three officers — A, B, C — respond on different days: Monday, Tuesday, Wednesday.

Clues:

A did not work Monday
B worked Tuesday
C did not work Wednesday

Construct table:

Officer	Monday	Tuesday	Wednesday
A	✘	?	?
B	?	✔	?
C	?	?	✘

Step 1: B is Tuesday

Remove Tuesday from others.

Officer	Monday	Tuesday	Wednesday
A	✘	✘	?
B	✘	✔	✘
C	?	✘	✘

Step 2: C cannot be Wednesday or Tuesday → must be Monday

Step 3: A must be Wednesday

Final Table:

Officer	Monday	Tuesday	Wednesday
A	✘	✘	✔
B	✘	✔	✘
C	✔	✘	✘

Answer:
C – Monday
B – Tuesday
A – Wednesday

UNIT 7: Speed Under Pressure (Timed Reasoning Tip)

In aptitude exams:

Do simple sequences first
Skip long logic puzzles temporarily
Return after completing easier questions
Avoid spending more than 60–90 seconds per question

TEACHER SUMMARY

Logical & Abstract Reasoning improves:

Pattern detection
Structured thinking
Analytical speed
Decision-making accuracy

These skills are critical for high-pressure environments such as emergency response.

MODULE 7: BASIC FIRE SERVICE & SAFETY AWARENESS

Overview

This module introduces the structure, mandate, and operations of the Ghana National Fire Service. It equips candidates with foundational knowledge of fire prevention, fire behavior, and safety protocols.

UNIT 1: Mandate of GNFS

The GNFS was established to:

Prevent and manage fire outbreaks.
Protect life and property.
Conduct fire safety education.
Provide rescue services.

Legal Basis:
Established under national law to operate as Ghana’s primary fire authority.

UNIT 2: Core Functions of the Fire Service

Function	Explanation
Fire Suppression	Extinguishing fires
Rescue Operations	Saving trapped victims
Public Education	Fire safety awareness
Inspection	Checking buildings for compliance
Investigation	Determining cause of fire

UNIT 3: Fire Prevention Strategies

Fire prevention reduces risk before fire occurs.

Prevention Methods:

Electrical safety checks
Proper storage of flammable materials
Installation of smoke detectors
Public awareness campaigns

UNIT 4: Common Causes of Fire

Cause	Explanation
Electrical faults	Overloaded circuits
Gas leaks	Poor cylinder handling
Open flames	Candles, cooking
Arson	Deliberate setting
Negligence	Carelessness

UNIT 5: Basic Fire Safety Equipment

Equipment	Function
Fire Extinguisher	Puts out small fires
Smoke Detector	Detects smoke
Fire Blanket	Smothers fire
Hose Reel	Directs water
Fire Alarm	Alerts occupants

Classes of Fire

Class	Fuel Type	Extinguishing Method
A	Wood, paper	Water
B	Flammable liquids	Foam
C	Gas	Dry Powder
D	Metals	Special powder
Electrical	Live equipment	CO₂

UNIT 6: Fire Triangle

Fire requires three elements:

Fuel
Heat
Oxygen

If one is removed, fire stops.

Diagram Representation:

Fuel + Heat + Oxygen = Fire

UNIT 7: Emergency Response Procedures

Standard Procedure:

Raise alarm
Evacuate area
Call emergency services
Use extinguisher (if trained)
Assemble at safe point

Chain of Command Concept

In uniformed services:

Level	Role
Officer-in-Charge	Leads operation
Station Officer	Manages station
Firefighter	Executes tasks

Professional Conduct

Fire officers must demonstrate:

Discipline
Integrity
Teamwork
Respect for authority
Calmness under pressure

MODULE 6: LOGICAL & ABSTRACT REASONING

Overview

UNIT 1: Number Sequences

Concept Explanation

Common Types of Number Sequences

1. Arithmetic Sequence

2. Geometric Sequence

UNIT 2: Letter Series

Concept Explanation

Example 1:

Example 2 (Alternating Pattern):

Teaching Tip:

UNIT 3: Pattern Recognition

Concept Explanation

Example:

UNIT 4: Analogies

Concept Explanation

Types of Analogies

Solving Strategy

UNIT 5: Deductive Reasoning

Concept Explanation

Example:

Common Logical Forms

UNIT 6: Logical Problem Solving

Concept Explanation

Teaching Approach

Importance for Fire Service

(Worked Examples and Structured Solutions)

UNIT 1: Number Sequences

1.1 Arithmetic Sequences

Definition

Formula

Worked Example 1

Worked Example 2

1.2 Geometric Sequences

Definition

Formula

Worked Example 3

1.3 Alternating Sequences

Worked Example 4

UNIT 2: Letter Series

Worked Example 5

Worked Example 6 (Alternating)

UNIT 3: Pattern Recognition

Types of Visual Patterns

Worked Example 7 (Rotation Concept)

Worked Example 8 (Element Increase)

UNIT 4: Analogies

Common Relationship Types

Worked Example 9

Worked Example 10

UNIT 5: Deductive Reasoning

Logical Forms

Worked Example 11

Worked Example 12

UNIT 6: Logical Problem Solving

Strategy

Worked Example 13

UNIT 7: Speed Under Pressure (Timed Reasoning Tip)

TEACHER SUMMARY

MODULE 7: BASIC FIRE SERVICE & SAFETY AWARENESS

Overview

UNIT 1: Mandate of GNFS

UNIT 2: Core Functions of the Fire Service

UNIT 3: Fire Prevention Strategies

Prevention Methods:

UNIT 4: Common Causes of Fire

UNIT 5: Basic Fire Safety Equipment

Classes of Fire

UNIT 6: Fire Triangle

UNIT 7: Emergency Response Procedures

Standard Procedure:

Chain of Command Concept

Professional Conduct

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