Grade 12 Maths · Number Patterns, Sequences and Series

Calculate an arithmetic series sum

Add the terms of a pattern with a constant difference using Sn = n/2[2a + (n − 1)d], for example 1 + 2 + … + 100 = 5 050.

past paper questions use it: 18 past paper questions use it
videos: 3 videos

Learn it: calculate an arithmetic series sum

Pick one and watch it, then try the questions below. Videos load only when you tap play.

7) Sum of Arithmetic Series Gr 12 | IntroKevinmathscience

7d) Sum of Arithmetic Series Gr 12 | TryKevinmathscience

Arithmetic Series: Sequences and Series - Grade 12Mindset

Now try it on a real exam question

No sign-up. Takes 3 minutes.

Question 2.2 · March 2023 · Provincial · 2 marks

The first four (4) terms of a quadratic pattern are:

11; 20; 33; 50; ...

2.2 Prove that the sum of the first

n

first-differences of this quadratic pattern can be given by

S_{n} = 2 n^{2} + 7 n

.(2)

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

More past paper questions: calculate an arithmetic series sum

Work each one out first, then open the memo and check every tick.

3. 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
4. Question 1.1.2 · March 2025 · Provincial · 2 marks
Consider the arithmetic sequence: $8; 15; 22; ...$
1.1 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
5. 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
6. Question 2.1.2 · March 2023 · Provincial · 2 marks
$10; a; 24; b; 38; ...$ are the first five terms of an arithmetic progression.
2.1 Arithmetic progression questions
2.1.2 Calculate the sum of the first 67 terms of the sequence.(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute into sum formula $a = 10, d = 7, n = 67$
  $S_{67} = \frac{67}{2} [2 (10) + (67 - 1) (7)]$
  1 mark · Calculate an arithmetic series sum
2. ✓
  Calculate final answer $S_{67} = 16147$
  1 mark · Calculate an arithmetic series sum

Free on Android

Know exactly which skill is costing you marks.

Mark past papers tick by tick in the NavyBlue app. It remembers every mark you lose, shows you the skills to fix first, and picks your next questions.

The NavyBlue app showing a learner's weak skills