Grade 12 Maths · Number Patterns, Sequences and Series

Read and write sigma notation

Read and write sums using the Σ sign, for example Σ 2n from n = 1 to 4 means 2 + 4 + 6 + 8, which has 4 terms.

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14) Sigma Grade 12 | IntroKevinmathscience

14r) Sigma Grade 12 | TryKevinmathscience

15b) Represent sigma notation | TryKevinmathscience

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Question 2.2 · May/June 2024 · Paper 1 · National (DBE) · 5 marks

2.2 Given:

\sum_{p = k}^{10} 3^{p - 1} = 29520

. Calculate the value of

k

.(5)

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More past paper questions: read and write sigma notation

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3. Question 2.1.2 · November 2024 · Paper 1 · National (DBE) · 4 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.
2.1.2 The original arithmetic series is extended to 75 terms. The sum of these 75 terms is 14 400. Using sigma notation, write down an equation for the sum of the terms added to the original series.(4)
Show the memo (3 ticks)Memo
1. ✓
  Determine general term of series $T_{n} = 7 + (n - 1) 5$
  $T_{n} = 5 n + 2$
  1 mark · Find a linear general term
2. ✓
  Calculate sum of added terms $S_{a dd e d} = S_{75} - S_{20}$
  $S_{a dd e d} = 14400 - 1090 = 13310$
  1 mark · Split a combined sequence
3. ✓
  Construct sigma notation equation $\sum_{n = 21}^{75} (5 n + 2) = 13310$
  2 marks · Read and write sigma notation
4. Question 2.1.1 · March 2025 · Provincial · 2 marks
2.1 Given: $\sum_{k = 2}^{13} (- 3)^{k}$
2.1.1 Write down the values of the first three terms of the series.(2)
Show the memo (2 ticks)Memo
1. ✓
  Calculate first term (k=2) $(- 3)^{2} = 9$
  1 mark · Read and write sigma notation
2. ✓
  Calculate next two terms (k=3, 4) $(- 3)^{3} = - 27$ ; $(- 3)^{4} = 81$
  1 mark · Read and write sigma notation
5. 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
6. Question 3.2 · March 2022 · Provincial · 4 marks
3.2 Evaluate: $\sum_{k = 1}^{20} 3^{k - 2}$ (4)
Show the memo (3 ticks)Memo
1. ✓
  Identify series parametersFirst term ( $k = 1$ ): $3^{1 - 2} = 3^{- 1} = \frac{1}{3}$
  Common ratio $r = 3$
  Number of terms $n = 20$
  2 marks · Read and write sigma notation
2. ✓
  Calculate sum $S_{20} = \frac{\frac{1}{3} ( 3 ^{20} - 1 )}{3 - 1}$
  1 mark · Calculate a geometric series sum
3. ✓
  Final answer $S_{20} = 581130733, 3$ (or equivalent fraction)
  1 mark · Calculate a geometric series sum

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