Grade 12 Maths · Number Patterns, Sequences and Series · Find x so terms form a pattern

Find x so terms form a pattern Grade 12

Find the unknown that makes given terms part of a pattern by setting the differences equal (arithmetic), the ratios equal (geometric) or the second differences equal (quadratic), for example 3; x; 11 arithmetic gives x - 3 = 11 - x, so x = 7.

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2) Solve X Arithmetic Sequence | IntroKevinmathscience

5) Solve X Geometric Sequence | IntroKevinmathscience

Grade 12 Maths Geometric Sequences Finding the value of xEducore

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Question 3.1 · May/June 2023 · Paper 1 · National (DBE) · 6 marks

3.1 Show that the general term of the sequence is

T_{n} = 5 n^{2} - 15 n + 16

.(6)

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

More past paper questions: find x so terms form a pattern

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3. Question 2.1.1 · November 2025 · Paper 1 · National (DBE) · 3 marks
2.1 Given the infinite geometric series: $(t + 10) + (t - 2) + (t + 4) + \dots$
2.1.1 Show that $t = - 2$ (3)
Show the memo (3 ticks)Memo
1. ✓
  Equating the ratios $\frac{t - 2}{t + 10} = \frac{t + 4}{t - 2}$
  1 mark · Find x so terms form a pattern
2. ✓
  Cross multiplication $(t - 2)^{2} = (t + 4) (t + 10)$
  1 mark · Clear fractions in an equation
3. ✓
  Expansion $t^{2} - 4 t + 4 = t^{2} + 14 t + 40$
  $- 18 t = 36$
  $∴ t = - 2$
  1 mark · Multiply two binomials
4. Question 3.1.1 · September 2024 · Paper 1 · Provincial · 2 marks
3.1 The first three terms of a geometric sequence are given: $81; m; \frac{m}{3}; \dots$
3.1.1 Determine the value of $m$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  $\frac{m}{81} = \frac{m /3}{m}$ $\frac{m}{81} = \frac{\frac{m}{3}}{m}$
  1 mark · Find x so terms form a pattern
2. ✓
  Answer $\frac{m}{81} = \frac{1}{3}$
  $3 m = 81$
  $m = 27$
  
  OR $m^{2} = \frac{81 m}{3}$ , $m^{2} = 27 m$ , $m = 27$
  1 mark · Find x so terms form a pattern
5. Question 3.1.1 · September 2024 · Paper 1 · Provincial · 2 marks
3.1 Given the arithmetic sequence: $10 x + 6; 2 x + 4; 4 x - 8$

Answer the questions that follow.
3.1.1 Determine the value of $x$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Equating $(2 x + 4) - (10 x + 6) = (4 x - 8) - (2 x + 4)$
  1 mark · Find x so terms form a pattern
2. ✓
  $x = 1$ $- 8 x - 2 = 2 x - 12$
  $- 10 x = - 10$
  $x = 1$
  1 mark · Find x so terms form a pattern
6. Question 2.1.1 · March 2023 · Provincial · 2 marks
2.1 $10; a; 24; b; 38; ...$ are the first five terms of an arithmetic progression.

Arithmetic progression questions
2.1.1 Show that $a = 17$ and $b = 31$ .(2)
Show the memo (2 ticks)Memo
1. ✓
  Calculate a using arithmetic mean or difference $a - 10 = 24 - a$ OR $a = \frac{10 + 24}{2}$
  $2 a = 34 ⟹ a = 17$
  1 mark · Find x so terms form a pattern
2. ✓
  Calculate b using arithmetic mean or difference $b - 24 = 38 - b$ OR $b = \frac{24 + 38}{2}$
  $2 b = 62 ⟹ b = 31$
  1 mark · Find x so terms form a pattern

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