Grade 12 Maths · Number Patterns, Sequences and Series · Use sequences and series in real life

Use sequences and series in real life Grade 12

Model a real situation, like a salary increase, a training plan or a bouncing ball, as an arithmetic or geometric sequence or series and choose the right formula to answer the question.

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Grade 12 Sequences and Series Part 3e AS Word ProblemLisa Oswald

Sequences and Series: Word Problems (Arithmetic Progressions)Oninab Academy

Exam Question Series SequencesKevinmathscience

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Question 3.2 · March 2023 · Provincial · 4 marks

3.2 Mr Peter gave his four sons R8400 to share, such that their shares formed terms of a geometric sequence. The largest share was 27 times the smallest share. Determine the amount each son received.(4)

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3. 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 (3 ticks)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 · Use sequences and series in real life
4. Question 3.2.2 · September 2026 · Paper 1 · Provincial · 3 marks
3.2 Shoba's annual salary is 150 000 and her expenses total R105 000. Her salary increases by R13 500 each year while her expenses increase by R17 000 each year. Each year she saves the excess of her income.

Answer the questions that follow.
3.2.2 If she continues to manage her finances this way, after how many years will she have nothing left to save?(3)
Show the memo (3 ticks)Memo
1. ✓
  METHOD 1: Income and expenses formulaeIncome $= 150000 + 13500 (n - 1)$
  Expenses $= 105000 + 17000 (n - 1)$
  1 mark · Find a linear general term
2. ✓
  METHOD 1: EquatingTo be left with nothing means INCOME = EXPENSES
  $150000 + 13500 (n - 1) = 105000 + 17000 (n - 1)$
  1 mark · Use sequences and series in real life
3. ✓
  METHOD 1: Answer $45000 = 3500 (n - 1)$
  $∴ n = 13, 86$ , so $n = 14$ years
  1 mark · Use sequences and series in real life
5. Practice · NavyBlue · 2 marks
Lerato trains for a race. She runs $5$ km on the first day and increases her distance by $0, 5$ km every day.
How far does she run on day $20$ ?(2)
Show the memo (2 ticks)Memo
1. ✓
  ModelArithmetic: $a = 5$ , $d = 0, 5$
  1 mark · Use sequences and series in real life
2. ✓
  Answer $T_{20} = 5 + 19 (0, 5) = 14, 5$ km
  1 mark · Find a linear general term
6. Practice · Siyavula Grade 12 Maths · Ex 2.12 · 2 marks
At 8 a.m. a local celebrity tweets about his new music album to $100$ of his followers. Five minutes later, each of his followers retweet his message to two of their friends. Five minutes after that, each friend retweets the message to another two friends. Assume this process continues.
(b) Calculate how many retweets of the celebrity's message are sent an hour after his original tweet. ( $1$ hour $= 60$ minutes $= 12 \times 5$ , therefore $n = 12$ .)(2)
Show the memo (2 ticks)Memo
1. ✓
  Substitute n = 12 $T_{12} = 100 \times 2^{11}$
  1 mark · Find a geometric sequence term
2. ✓
  Answer $= 204800$ retweets
  1 mark · Use sequences and series in real life
Question adapted from Siyavula Education (CC BY 3.0) · Solution by NavyBlue

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