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

Applications of Sequences and Series Grade 12

Real Applications of Sequences and Series past paper questions and answers from 2021 to 2024, with each memo split into the ticks examiners give. Try one, mark yourself, and see exactly which skill cost you marks.

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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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Applications of Sequences and Series skills

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Split a combined sequenceSeparate a sequence that mixes two patterns into its two parts, for example 1, 2, 3, 4, 5, 8 splits into 1, 3, 5 and 2, 4, 8.10 past paper questions · 4 videos

More Applications of Sequences and Series Grade 12 questions and answers

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4. Question 2.1.3 · March 2024 · Paper 1 · Provincial · 4 marks
2.1 The given number pattern is a combination of a quadratic sequence and an arithmetic sequence: $16; 32; 0; 28; - 12; 24; - 20; 20; \dots$
2.1.3 The given number pattern has two consecutive terms that are equal in value. Determine the positions of the two terms.(4)
Show the memo (4 ticks)Memo
1. ✓
  Equate the two general terms $2 n^{2} - 22 n + 36 = - 4 n + 36$
  1 mark · Set up an expression or equation
2. ✓
  Simplify and factorize $2 n^{2} - 18 n = 0$
  $n^{2} - 9 n = 0$
  $n (n - 9) = 0$
  1 mark · Take out a common factor
3. ✓
  Identify valid solution for n $n = 9$ (since $n = 0$ is invalid for position)
  1 mark · Solve a quadratic by factorising
4. ✓
  Determine term positions in combined patternThe terms are in positions $2 n - 1$ and $2 n$ .
  If $n = 9$ , positions are $17$ and $18$ .
  Answer: $T_{17}$ and $T_{18}$
  1 mark · Split a combined sequence
5. Question 2.1.3 · March 2023 · Provincial · 3 marks
2.1 $10; a; 24; b; 38; ...$ are the first five terms of an arithmetic progression.

Arithmetic progression questions
2.1.3 If there are 67 terms in this arithmetic sequence, determine the sum of all the even terms of this sequence.(3)
Show the memo (3 ticks)Memo
1. ✓
  Sequence of the even terms $10; 24; 38; 52; 66; ...$
  $a = 10$ ; $d = 14$ ; $n = 34$
  1 mark · Split a combined sequence
2. ✓
  Substitute into the sum formula $S_{n} = \frac{n}{2} [2 a + (n - 1) d]$
  $S_{34} = \frac{34}{2} [2 (10) + (34 - 1) (14)]$
  1 mark · Calculate an arithmetic series sum
3. ✓
  Answer $S_{34} = 8194$
  1 mark · Calculate an arithmetic series sum
6. Question 2.1.2 · March 2021 · Provincial · 5 marks
2.1 In the diagram, $△ PQR$ is given such that $QT = 3$ units, $T V = 5$ units, $TR = 8$ units and $ST ∥ P V$ . Determine the following with reasons:
2.1.2 Calculate $\frac{Area Δ PQR}{Area of quadrilateral PSTR}$ (5)
Show the memo (5 ticks)Memo
1. ✓
  Define lengths based on ratioLet $QS = 3 a$ and $QP = 8 a$ (from 2.1.1 ratio)
  0 marks · Use a ratio, rate or proportion
2. ✓
  Calculate Area PQRArea $Δ PQR = \frac{1}{2} \times QP \times QR sin \hat{Q}$
  $= \frac{1}{2} \times 8 a \times 11 sin \hat{Q}$
  $= 44 a sin \hat{Q}$
  1 mark · Use the area rule
3. ✓
  Calculate Area SQTArea $Δ SQT = \frac{1}{2} \times 3 a \times 3 sin \hat{Q}$
  1 mark · Use the area rule
4. ✓
  Calculate Area PSTRArea quad $PSTR = Area Δ PQR - Area Δ SQT$
  $= 44 a sin \hat{Q} - \frac{9}{2} a sin \hat{Q}$
  $= \frac{79}{2} a sin \hat{Q}$
  1 mark · Calculate area or perimeter
5. ✓
  Calculate final ratio $\frac{Area Δ PQR}{Area quad PSTR} = \frac{44 a s i n Q ^}{\frac{79}{2} a s i n Q ^} = \frac{88}{79}$
  2 marks · Simplify an algebraic fraction

Applications of Sequences and 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

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