Grade 10 Maths · Number Patterns, Sequences and Series

Continue a number pattern

Find how a number pattern grows and write the next terms, for example 3, 7, 11, 15 adds 4 each time, so the next term is 19.

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Determine the rule of a numeric pattern grade 8 mathematicsALRI PRINSLOO

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Question 3.1 · November 2024 · Paper 1 · National (DBE) · 2 marks

A circle with radius

6

cm is drawn. A second, smaller circle is drawn through the centre of the first circle and also touches the first circle internally, as shown in the diagram. A third, smaller circle is drawn through the centre of the second circle and touches the second circle internally. The process of drawing circles continues and forms a geometric pattern. Diagram for this question

3.1 Write down the radius of the

3^{rd}

circle.(2)

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

More past paper questions: continue a number pattern

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3. Question 1.1.1 · March 2022 · Provincial · 2 marks
1.1 Consider: $9; 19; 33; 51; \dots$
1.1.1 Write the next TWO terms of the pattern.(2)
Show the memo (3 ticks)Memo
1. ✓
  Identify first and second differencesFirst differences: $10; 14; 18$
  Second difference: $4$
  0 marks · Continue a number pattern
2. ✓
  Fifth term $T_{5} = 51 + (18 + 4) = 73$
  1 mark · Continue a number pattern
3. ✓
  Sixth term $T_{6} = 73 + (22 + 4) = 99$
  1 mark · Continue a number pattern
4. Question 1.1 · March 2021 · Provincial · 2 marks
Given the quadratic sequence: $44; 52; 64; 80; \dots$
1.1 Write down the next two terms of the sequence.(2)
Show the memo (3 ticks)Memo
1. ✓
  Determine differencesFirst differences: $52 - 44 = 8$ ; $64 - 52 = 12$ ; $80 - 64 = 16$
  Second difference: $4$
  0 marks · Continue a number pattern
2. ✓
  Fifth term $T_{5} = 80 + (16 + 4) = 100$
  1 mark · Continue a number pattern
3. ✓
  Sixth term $T_{6} = 100 + (20 + 4) = 124$
  1 mark · Continue a number pattern
5. Question 4.1 · March 2021 · Provincial · 2 marks
In the diagram, the $1^{s t}$ (outer) triangle is an equilateral triangle with sides of $8$ cm. A $2^{n d}$ triangle is drawn within this triangle by joining the midpoints of the sides of the $1^{s t}$ triangle. This process is continued without end.
4.1 What is the perimeter of the $4^{t h}$ triangle?(2)
Show the memo (1 tick)Memo
1. ✓
  Determine sequence of perimeters $P_{1} = 3 \times 8 = 24$
  Sides halve each time: $8; 4; 2; 1$
  $P_{2} = 12, P_{3} = 6, P_{4} = 3$
  2 marks · Continue a number pattern
6. Question 3.1.1 · March 2018 · Provincial · 2 marks
3.1 Consider the following quadratic number pattern: $64; 42; 24; ...$
3.1.1 Write down the next TWO terms of the number pattern.(2)
Show the memo (1 tick)Memo
1. ✓
  Determine differencesFirst diffs: $- 22; - 18$
  Second diff: $4$
  Next first diffs: $- 14; - 10$
  Terms: $24 - 14 = 10$ and $10 - 10 = 0$
  2 marks · Continue a number pattern

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