Number Patterns: Grade 10 Mathematics Master
Study Guide
This comprehensive study guide covers everything you need to master number patterns for Grade 10 Mathematics. From
linear arithmetic sequences to geometric patterns, quadratic rules, and cyclical power analysis, each section builds your
understanding step by step. Worked examples, examination-style questions, and a full marking memorandum are included
to prepare you thoroughly for any assessment.
GRADE 10 MATHEMATICS NUMBER PATTERNS EXAM PREPARATION
© E-Loné Scheepers 2026
,Guide Overview
This guide is structured into five major chapters. Use this overview to navigate between topics and track your progress as
you study.
01 02 03
Linear Number Patterns Non-Linear & Special Patterns Comprehensive Worked
Core concepts, the general formula Quadratic (square) patterns, Examples
Tn = dn + c, methods for finding Tn ,
geometric/exponential sequences, Three fully worked multi-step
algebraic variables, and common dual interleaved sequences, and examples covering linear sequences,
pitfalls. cyclical power analysis. geometric visual patterns, and cyclical
power analysis.
04 05
Examination-Style Test Detailed Marking Memorandum
A full 60-minute, 50-mark practice paper with four Complete solutions with mark allocations for every
questions covering all major pattern types. question in the practice test.
© E-Loné Scheepers 2026
, CHAPTER 1
Linear Number Patterns
A linear number pattern, also known as an arithmetic sequence, is one of the most fundamental concepts in Grade 10
Mathematics. It is an ordered list of numbers in which the difference between every pair of consecutive terms remains
exactly the same throughout the entire sequence. This fixed, unchanging difference is what makes the pattern "linear" —
when you plot the terms against their positions on a graph, the points lie along a straight line.
Understanding linear patterns is essential not only for this topic but also for algebra, functions, and financial mathematics
that you will encounter in higher grades. The skills you develop here — setting up equations, identifying structure, and
generalising rules — are used across the entire mathematics curriculum.
© E-Loné Scheepers 2026
, Key Terminology & Symbols
Before applying any formula, you must be confident with the language of sequences. Each symbol has a precise meaning,
and confusing them is one of the most common sources of errors in examinations.
Symbol Name / Concept Definition / Description Domain / Restriction
n Term Position The ordinal position of a term in the n ∈ N = {1, 2, 3, … } (Must
sequence (e.g., 1st, 2nd, 3rd). be a positive integer)
Tn General Term The actual value of the term at position n. Tn ∈ R (Real numbers)
d Common The fixed value added to each term to d = T2 − T1 = T3 − T2 =
Tn − Tn−1
Difference produce the next term.
c Constant Term The vertical intercept / offset term in the c = T1 − d, or the
general rule. theoretical 0th term T0
Always distinguish carefully between n (the position) and Tn (the value). These are not interchangeable.
© E-Loné Scheepers 2026
Study Guide
This comprehensive study guide covers everything you need to master number patterns for Grade 10 Mathematics. From
linear arithmetic sequences to geometric patterns, quadratic rules, and cyclical power analysis, each section builds your
understanding step by step. Worked examples, examination-style questions, and a full marking memorandum are included
to prepare you thoroughly for any assessment.
GRADE 10 MATHEMATICS NUMBER PATTERNS EXAM PREPARATION
© E-Loné Scheepers 2026
,Guide Overview
This guide is structured into five major chapters. Use this overview to navigate between topics and track your progress as
you study.
01 02 03
Linear Number Patterns Non-Linear & Special Patterns Comprehensive Worked
Core concepts, the general formula Quadratic (square) patterns, Examples
Tn = dn + c, methods for finding Tn ,
geometric/exponential sequences, Three fully worked multi-step
algebraic variables, and common dual interleaved sequences, and examples covering linear sequences,
pitfalls. cyclical power analysis. geometric visual patterns, and cyclical
power analysis.
04 05
Examination-Style Test Detailed Marking Memorandum
A full 60-minute, 50-mark practice paper with four Complete solutions with mark allocations for every
questions covering all major pattern types. question in the practice test.
© E-Loné Scheepers 2026
, CHAPTER 1
Linear Number Patterns
A linear number pattern, also known as an arithmetic sequence, is one of the most fundamental concepts in Grade 10
Mathematics. It is an ordered list of numbers in which the difference between every pair of consecutive terms remains
exactly the same throughout the entire sequence. This fixed, unchanging difference is what makes the pattern "linear" —
when you plot the terms against their positions on a graph, the points lie along a straight line.
Understanding linear patterns is essential not only for this topic but also for algebra, functions, and financial mathematics
that you will encounter in higher grades. The skills you develop here — setting up equations, identifying structure, and
generalising rules — are used across the entire mathematics curriculum.
© E-Loné Scheepers 2026
, Key Terminology & Symbols
Before applying any formula, you must be confident with the language of sequences. Each symbol has a precise meaning,
and confusing them is one of the most common sources of errors in examinations.
Symbol Name / Concept Definition / Description Domain / Restriction
n Term Position The ordinal position of a term in the n ∈ N = {1, 2, 3, … } (Must
sequence (e.g., 1st, 2nd, 3rd). be a positive integer)
Tn General Term The actual value of the term at position n. Tn ∈ R (Real numbers)
d Common The fixed value added to each term to d = T2 − T1 = T3 − T2 =
Tn − Tn−1
Difference produce the next term.
c Constant Term The vertical intercept / offset term in the c = T1 − d, or the
general rule. theoretical 0th term T0
Always distinguish carefully between n (the position) and Tn (the value). These are not interchangeable.
© E-Loné Scheepers 2026
