∑ DANEMATHICS
FREE CAPS MATHS RESOURCES
Grade 9 · Patterns
Number Patterns: Finding and Using the Rule
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.
- 1Find the rule for 7, 10, 13, 16, … (find rule)(2)d = 3; 3(1)+c = 7 → c = 4; Tₙ = 3n + 4✓✓ (2)
- 2Find the rule for 2, 6, 10, 14, … (find rule)(2)d = 4; 4(1)+c = 2 → c = −2; Tₙ = 4n − 2✓✓ (2)
- 3For Tₙ = 5n + 1, find the 10th term. (far term)(2)5(10)+1 = 51✓✓ (2)
- 4Find the 100th term of 4, 7, 10, … (far term)(2)Tₙ = 3n+1; T₁₀₀ = 301✓✓ (2)
- 5Which term of 4, 7, 10, … equals 100? (work back)(2)3n+1 = 100 → 3n = 99 → n = 33rd term✓✓ (2)
- 6Which term of 5, 9, 13, … equals 81? (work back)(2)4n+1 = 81 → n = 20th term✓✓ (2)
- 7Find the rule for 30, 25, 20, 15, … (decreasing)(2)d = −5; −5+c = 30 → c = 35; Tₙ = −5n + 35✓✓ (2)
- 8Find the rule for 12, 9, 6, 3, … (decreasing)(2)d = −3; c = 15; Tₙ = −3n + 15✓✓ (2)
- 9The tile pattern below grows in the same way each time. Determine a rule for the number of tiles in the n-th term.(2)d = 3, c = 2; Tₙ = 3n + 2✓✓ (2)
- 10Is 45 a term of 3, 7, 11, …? (check)(2)4n−1 = 45 → 4n = 46 → n = 11,5, not whole → No✓✓ (2)
TOTAL: 20 marks