Mathbench

Matric past papers · DBE (CAPS) · Paper 1

DBE Grade 12 Patterns, sequences and series

Every patterns, sequences and series question from the DBE NSC Paper 1 papers of November 2021–2024 and May/June 2021, 2022, 2024, 2025, in one booklet — 17 questions, 205 marks, with the official marking guideline for every one of them. Free to download, in English and Afrikaans.

Download

Each question is a clip of the original DBE page: the wording, the mark allocations and the diagrams are exactly as they were printed. Only the blank answer space has been removed, so work in a separate book. The solutions booklet is the board’s own marking guideline, not a rewritten one.

What is in it

17 questions in 3 chapters, ordered so you can work through one skill at a time.

#QuestionSkillsMarksFrom
1A quadratic pattern, a difference of 33, then adding m to every termQuadratic patterns and second differences, Finding the general term Tn9May/June 2025 Q3
2Find b from the first difference, then the 60th termQuadratic patterns and second differences, Finding the general term Tn10November 2022 Q3
3A pattern that turns, and where its terms start to fallQuadratic patterns and second differences, Finding the general term Tn11November 2021 Q3
43 ; 7 ; 12 ..., then what must be added to reach 13 527Quadratic patterns and second differences, Finding the general term Tn, Arithmetic sequences and series15May/June 2024 Q3
5When a term of the pattern equals a term of its own differencesQuadratic patterns and second differences, Finding the general term Tn17May/June 2021 Q2
6A linear pattern, its sum, and a sigma expansionArithmetic sequences and series, Summing the first n terms, Sigma notation10November 2021 Q4
7Twenty terms, then seventy-five, and the term that had to changeArithmetic sequences and series, Summing the first n terms, Solving for n14November 2024 Q2
8From the 7th term to the number of terms, then the first fortyArithmetic sequences and series, Solving for n, Summing the first n terms16May/June 2022 Q2
9T91 and S91, then a quadratic pattern from three differencesArithmetic sequences and series, Summing the first n terms, Solving for n, Quadratic patterns and second differences16November 2023 Q2
10An athlete's weekly kilometres as an arithmetic seriesArithmetic sequences and series, Summing the first n terms, A sequence modelling something real18May/June 2025 Q2
11Find x, show the sum formula, then the sum to infinityGeometric sequences and series, Summing the first n terms, Convergence and the sum to infinity6November 2021 Q2
12The general term, then which term of the series equals 15 625Geometric sequences and series, Finding the general term Tn, Solving for n9May/June 2021 Q3
13Does it converge? Then k from a sigma that comes to 29 520Convergence and the sum to infinity, Geometric sequences and series, Sigma notation9May/June 2024 Q2
14k from a sum of 98 301, then a geometric and an arithmetic togetherGeometric sequences and series, Sigma notation, Arithmetic sequences and series10November 2023 Q3
15Circles inside circles, and the series their radii makeGeometric sequences and series, Convergence and the sum to infinity, A sequence modelling something real10November 2024 Q3
16The 10th term, then the values of t that let it convergeGeometric sequences and series, Sigma notation, Convergence and the sum to infinity11May/June 2022 Q3
17r from the 6th term, then how many terms reach 114 674Geometric sequences and series, Summing the first n terms, Solving for n14November 2022 Q2