Grade 10 Maths · Number Patterns, Sequences and Series

Find a linear general term

Write a formula for any term of a pattern that adds the same amount each time, for example 5, 8, 11, … gives Tn = 3n + 2.

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Determine the rule of a numeric pattern grade 9 mathematicsALRI PRINSLOO

Determine the rule of a numeric pattern grade 8 mathematicsALRI PRINSLOO

1) Gr 12 Arithmetic Sequence | IntroKevinmathscience

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Question 3.1.3 · November 2024 · Paper 1 · Provincial · 2 marks

3.1 In each diagram below, there are shaded squares and white squares. Diagram for this question

3.1.3 Which diagram will consist of 1 500 shaded squares?(2)

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More past paper questions: find a linear general term

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3. Question 3.2.1 · May/June 2024 · Paper 1 · National (DBE) · 3 marks
3.2 Given an arithmetic sequence with $T_{1} = 8$ and $T_{2} = 11$ .
3.2.1 Calculate $n$ if $T_{n} = 41$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Determine general term equation $T_{n} = 3 n + 5$
  1 mark · Find a linear general term
2. ✓
  Equate to target value $41 = 3 n + 5$
  1 mark · Find a linear general term
3. ✓
  Final n-value $n = 12$
  1 mark · Find a linear general term
4. Question 2.1.2 · March 2025 · Provincial · 2 marks
The given number pattern is a combination of a quadratic sequence and an arithmetic sequence: $16; 32; 0; 28; - 12; 24; - 20; 20; ...$
2.1 Pattern analysis questions.
2.1.2 Determine the general term of the arithmetic sequence.(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify a and d and substituteSequence: $32; 28; 24; 20$
  $a = 32$ ; $d = - 4$
  $T_{n} = 32 + (n - 1) (- 4)$
  1 mark · Find a linear general term
2. ✓
  Simplify general term $T_{n} = - 4 n + 36$
  1 mark · Find a linear general term
5. Question 1.1.3 · March 2025 · Provincial · 3 marks
Consider the arithmetic sequence: $8; 15; 22; ...$
1.1 Consider the arithmetic sequence: $8; 15; 22; ...$
1.1.3 If it is given that $T_{72} + T_{72 - m} = 786$ , determine the value of $m$ .(3)
Show the memo (3 ticks)Memo
1. ✓
  Calculate T72 $T_{72} = 8 + (72 - 1) (7) = 505$
  1 mark · Find a linear general term
2. ✓
  Substitute and set up equation $T_{72 - m} = 8 + (72 - m - 1) (7)$
  $505 + 8 + 497 - 7 m = 786$
  1 mark · Find a linear general term
3. ✓
  Solve for m $- 7 m = - 224$
  $m = 32$
  1 mark · Find a linear general term
6. Question 1.1.1 · March 2024 · Paper 1 · Provincial · 2 marks
1.1 Consider the arithmetic sequence: $8; 15; 22; \dots$
1.1.1 Determine the $3 6^{th}$ term(2)
Show the memo (2 ticks)Memo
1. ✓
  Identify parameters and substitute into arithmetic general term formula $a = 8$
  $d = 7$
  $n = 36$
  $T_{n} = a + (n - 1) d$
  $T_{36} = 8 + (36 - 1) (7)$
  1 mark · Find a linear general term
2. ✓
  Calculate final answer $T_{36} = 253$
  1 mark · Find a linear general term

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