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Arithmetic and geometric sequences, series, sigma notation and financial applications.
Watch the full lesson before attempting practice questions.
Master these ideas before attempting exam questions.
Each term increases by a constant difference d. General term: Tₙ = a + (n−1)d.
Each term is multiplied by a constant ratio r. General term: Tₙ = a·rⁿ⁻¹.
Sum of n terms: Sₙ = n/2(2a + (n−1)d) or Sₙ = n/2(a + l).
Sum of n terms: Sₙ = a(rⁿ−1)/(r−1). If |r| < 1, infinite sum: S∞ = a/(1−r).
∑ notation is shorthand for a sum. Identify the general term and the range of values.
Commit these to memory — they appear in almost every exam.
These are your learning targets for Patterns & Sequences.
Avoid these errors — they cost marks every year.
The formula is a + (n−1)d, not a + nd. Off-by-one errors lose marks.
The infinite sum formula only works if the series converges. Always check |r| < 1 first.
Check the pattern: constant difference (arithmetic) vs. constant ratio (geometric).
Free CAPS-aligned study materials for Patterns & Sequences.
Comprehensive CAPS-aligned notes covering all key concepts, theorems, and worked examples for Patterns & Sequences.
NSC-style exam questions with full memorandum. Ideal for timed practice and self-assessment before exams.
Graded practice questions organised by difficulty. Perfect for building confidence before Paper 1.
Straight answers to common Grade 12 CAPS questions about Patterns and Sequences.
Patterns and Sequences in Grade 12 CAPS covers arithmetic sequences, geometric sequences, series, and sigma notation. You learn how to identify patterns, find terms, and calculate sums.
Start by deciding whether the pattern is arithmetic or geometric, then use the correct formula carefully. Regular practice helps you recognise the structure of questions much faster.
Common mistakes include mixing up arithmetic and geometric formulas, using the wrong term number, and confusing the nth term with the sum formula. Careless calculator input also causes errors.
CAPS exams usually test nth term, sum formulas, sigma notation, and practical pattern questions. These questions are common in Paper 1 and often connect to algebraic reasoning.
Book a focused session with Chris Khomo and work through this topic step by step — at your own pace, online, from anywhere in South Africa.