∑ DANEMATHICS
FREE CAPS MATHS RESOURCES
Grade 11–12 · Number Patterns, Sequences and Series
Quadratic Number Patterns (Grade 11 & 12)
MEMORANDUM
Name:
Class:
Date:
Mark
/ 17
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.
- 1Show that 3 ; 8 ; 17 ; 30 ; 47 is a quadratic pattern.(2)First differences 5 ; 9 ; 13 ; 17. Second differences 4 ; 4 ; 4 — constant, so it is quadratic.✓✓ (2)
- 2Determine Tₙ for 3 ; 8 ; 17 ; 30 ; 47(4)2a = 4 → a = 2; 3a + b = 5 → b = −1; a + b + c = 3 → c = 2. Tₙ = 2n² − n + 2✓✓✓✓ (4)
- 3Which term of 3 ; 8 ; 17 ; 30 ; 47 equals 122?(3)2n² − n − 120 = 0 → (2n + 15)(n − 8) = 0 → n = 8 (reject n = −7,5)✓✓✓ (3)
- 4Determine the general term of the pattern shown in the difference table below.(3)2a = 2 → a = 1; 3a + b = 4 → b = 1; a + b + c = 1 → c = −1. Tₙ = n² + n − 1✓✓✓ (3)
- 51 ; p ; 11 ; … is a quadratic pattern whose first differences are 3 ; 7 ; … Determine p.(2)p − 1 = 3, so p = 4✓✓ (2)
- 6The second difference of a quadratic pattern is 6. Determine a.(1)2a = 6, so a = 3✓ (1)
- 7Calculate T₁₀ if Tₙ = 2n² − n + 2.(2)2(100) − 10 + 2 = 192✓✓ (2)
TOTAL: 17 marks