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Grade 10 · Patterns
Number Patterns: Linear Sequences (Grade 10)
MEMORANDUM
Name:
Class:
Date:
Mark
/ 16
Answer all questions. Show all your working — marks are awarded for method as well as the final answer. Teacher copy: accept any correct equivalent method.
- 1Write down the constant difference of 5 ; 8 ; 11 ; 14 ; …(2)d = 3✓✓ (2)
- 2Determine the general term Tₙ of 5 ; 8 ; 11 ; 14 ; …(2)d = 3, T₁ = 5 → c = 2 → Tₙ = 3n + 2✓✓ (2)
- 3Calculate T₅₀ for the sequence 5 ; 8 ; 11 ; …(2)3(50) + 2 = 152✓✓ (2)
- 4Which term of 5 ; 8 ; 11 ; … is equal to 47?(2)3n + 2 = 47 → n = 15✓✓ (2)
- 5Is 100 a term of the sequence 5 ; 8 ; 11 ; …? Justify.(2)3n = 98 gives n = 32,67 which is not a whole number, so no.✓✓ (2)
- 6Determine the general term of 7 ; 11 ; 15 ; 19 ; …(2)d = 4, c = 3 → Tₙ = 4n + 3✓✓ (2)
- 7Determine the general term of 20 ; 17 ; 14 ; 11 ; …(2)d = −3, c = 23 → Tₙ = −3n + 23✓✓ (2)
- 8Explain why a linear sequence plots as a straight line.(2)Because Tₙ = dn + c is the equation of a straight line, with the constant difference as the gradient.✓✓ (2)
TOTAL: 16 marks