∑ DANEMATHICS
FREE CAPS MATHS RESOURCES
Grade 8 · Patterns
Pattern Rules: In Words and in Algebra
MEMORANDUM
Name:
Class:
Date:
Mark
/ 20
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.
- 1Describe in words the rule for 4, 9, 14, 19, …(2)Multiply the position number by 5, then subtract 1✓✓ (2)
- 2Determine the general rule (Tₙ) for 4, 9, 14, 19, …(2)d = 5, c = 4 − 5 = −1 → Tₙ = 5n − 1✓✓ (2)
- 3Determine the general rule for 7, 12, 17, 22, …(2)d = 5, c = 2 → Tₙ = 5n + 2✓✓ (2)
- 4Determine the general rule for 6, 11, 16, 21, …(2)d = 5, c = 1 → Tₙ = 5n + 1✓✓ (2)
- 5Determine the general rule for 30, 26, 22, 18, …(2)d = −4, c = 34 → Tₙ = −4n + 34✓✓ (2)
- 6For Tₙ = 4n + 3, find the 10th term.(2)4(10) + 3 = 43✓✓ (2)
- 7For Tₙ = 6n − 2, find the 25th term.(2)6(25) − 2 = 148✓✓ (2)
- 8Which term of 5, 9, 13, … equals 45?(2)Tₙ = 4n + 1; 4n + 1 = 45 → n = 11th term✓✓ (2)
- 9Is 100 a term of the pattern 3, 7, 11, …? Show your working.(2)Tₙ = 4n − 1; 4n − 1 = 100 → 4n = 101 → n = 25,25, not a whole number → No✓✓ (2)
- 10A pattern of matchsticks is 4, 7, 10, … Determine a rule for the number of sticks in shape n.(2)d = 3, c = 1 → Tₙ = 3n + 1✓✓ (2)
TOTAL: 20 marks