Grade 12 Maths · Number Patterns, Sequences and Series · Paper 1

Series Grade 12

Real Series past paper questions and answers from 2024 to 2025, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

past paper questions: 24 past paper questions
skills: 4 skills
videos: 4 videos

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Question 1.3 · November 2024 · Paper 1 · National (DBE) · 3 marks

1.3 Consider the product

(1 + \frac{1}{2}) (1 + \frac{1}{3}) (1 + \frac{1}{4}) ... (1 + \frac{1}{n})

. Determine ALL the values of

n

(

n \geq 2

) for which the product will be an integer value.(3)

Work it out on paper first. Then mark yourself with the official memo, one tick at a time.

Series skills

Each skill is one thing a memo gives a tick for. Tap one for its own questions, notes and videos.

More Series Grade 12 questions and answers

Try each one on paper before you open the memo.

4. Question 2.1.3 · May/June 2025 · Paper 1 · National (DBE) · 3 marks
2.1 Given the arithmetic series: $5 + 7 + 9 + ... + 93$

Answer the following based on the arithmetic series.
2.1.3 The athlete used this opportunity to raise funds for her high school. The community sponsored her $R 10$ for each kilometre run during the training programme. Calculate the total amount that the athlete raised for her school.(3)
Show the memo (1 tick)Memo
1. ✓
  Convert distance to money first, then sumSequence of money raised: $50 + 70 + 90 + ... + 930$
  $S_{45} = \frac{45}{2} [2 (50) + (45 - 1) (20)]$
  $S_{45} = R 22050$
  Total raised $= R 22050$
  3 marks · Calculate an arithmetic series sum
5. Question 2.1.1 · November 2024 · Paper 1 · National (DBE) · 2 marks
2.1 The first term of an arithmetic series is 7. The common difference of this series is 5 and the series contains 20 terms.
2.1.1 Calculate the sum of this series.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute into sum formula $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$
  $S_{20} = \frac{20}{2} [2 (7) + (19) (5)]$
  1 mark · Calculate an arithmetic series sum
2. ✓
  Calculate final answer $S_{20} = 1090$
  1 mark · Calculate an arithmetic series sum
6. Question 1.1.2 · March 2025 · Provincial · 2 marks
1.1 Consider the arithmetic sequence: $8; 15; 22; ...$

Consider the arithmetic sequence: $8; 15; 22; ...$
1.1.2 Calculate the sum of the first 36 terms.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute into sum formula $S_{36} = \frac{36}{2} [2 (8) + (36 - 1) (7)]$
  1 mark · Calculate an arithmetic series sum
2. ✓
  Calculate final answer $S_{36} = 4698$
  1 mark · Calculate an arithmetic series sum
7. Question 2.1.4 · March 2025 · Provincial · 3 marks
2.1 Given: $\sum_{k = 2}^{13} (- 3)^{k}$
2.1.4 Calculate $\sum_{k = 2}^{13} (- 3)^{k} x$ . Give your answer in terms of $x$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Identify series parametersThe series is $9 x - 27 x + 81 x ...$
  $a = 9 x$
  $r = - 3$
  $n = 13 - 2 + 1 = 12$
  1 mark · Read and write sigma notation
2. ✓
  Substitute into geometric sum formula $S_{12} = \frac{9 x (( - 3 ) ^{12} - 1 )}{- 3 - 1}$
  1 mark · Calculate a geometric series sum
3. ✓
  Calculate final answer $S_{12} = - 1195740 x$
  1 mark · Calculate a geometric series sum
8. Question 1.1.2 · March 2024 · Paper 1 · Provincial · 2 marks
1.1 Consider the arithmetic sequence: $8; 15; 22; \dots$
1.1.2 Calculate the sum of the first 36 terms.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute into the sum formula $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$
  $S_{36} = \frac{36}{2} [2 (8) + (36 - 1) (7)]$
  1 mark · Calculate an arithmetic series sum
2. ✓
  Calculate final sum $S_{36} = 4698$
  1 mark · Calculate an arithmetic series sum
9. Question 2.2 · March 2024 · Paper 1 · Provincial · 4 marks
2.2 Calculate: $\sum_{k = 3}^{9} 2 (- 3)^{k}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Determine the first term, ratio and number of terms $T_{1} = 2 (- 3)^{3} = - 54$
  $T_{2} = 2 (- 3)^{4} = 162$
  $a = - 54; r = - 3$
  $n = 9 - 3 + 1 = 7$
  2 marks · Read and write sigma notation
2. ✓
  Substitute into geometric sum formula $S_{7} = \frac{- 54 (( - 3 ) ^{7} - 1 )}{- 3 - 1}$
  1 mark · Calculate a geometric series sum
3. ✓
  Calculate final sum $S_{7} = - 29538$
  1 mark · Calculate a geometric series sum
10. Question 2.2 · September 2024 · Paper 1 · Provincial · 5 marks
2.2 Determine the sum of the whole numbers between 100 and 1 000 which are divisible by 11.(5)
Show the memo (5 ticks)Memo
1. ✓
  Series identification $110; 121; ...; 990$
  1 mark · Find a linear general term
2. ✓
  Substitute into Tn formula $990 = 110 + (n - 1) 11$
  1 mark · Find a linear general term
3. ✓
  Solve for n $n = 81$
  1 mark · Find a linear general term
4. ✓
  Substitute into Sn formula $S_{81} = \frac{81}{2} (110 + 990)$
  1 mark · Calculate an arithmetic series sum
5. ✓
  Answer $44550$
  1 mark · Calculate an arithmetic series sum

Series Grade 12 videos

Short lessons from South African teachers first. Videos load only when you tap play, to save your data.

Gr 12 Maths - Sequences and Series - 12 - Combined SequencesJuniorTukkie at the University of Pretoria

7) Sum of Arithmetic Series Gr 12 | IntroKevinmathscience

8) Sum of Geometric Series Gr 12 | IntroKevinmathscience

Euclidean geometry proofs in less than 10 minutes - Grade 11 and12 NSC & IEBMathew's Academy Of Sciences

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