Quadratic Number Patterns (Grade 11 & 12) — Worksheet & Memo

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Grade 12 · Patterns & Sequences

Quadratic Number Patterns (Grade 11 & 12)

MEMORANDUM

Name:

Class:

Date:

Mark

/ 14

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.

1
Show 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)
2
Determine Tₙ for 3 ; 8 ; 17 ; 30 ; 47
(2)
2a = 4 → a = 2; 3a + b = 5 → b = −1; a+b+c = 3 → c = 2. Tₙ = 2n² − n + 2✓✓ (2)
3
Which term of 3 ; 8 ; 17 ; 30 ; 47 equals 122?
(2)
2n² − n − 120 = 0 → (2n+15)(n−8) = 0 → n = 8 (reject n = −7,5)✓✓ (2)
4
Determine the general term of the pattern shown in the difference table below.
(2)
2a = 2 → a = 1; 3a + b = 4 → b = 1; a+b+c = 1 → c = −1. Tₙ = n² + n − 1✓✓ (2)
5
1 ; p ; 11 ; … is a quadratic pattern whose first differences are 3 ; 7 ; … Determine p.
(2)
p − 1 = 3, so p = 4✓✓ (2)
6
The second difference of a quadratic pattern is 6. Determine a.
(2)
2a = 6, so a = 3✓✓ (2)
7
Calculate T₁₀ if Tₙ = 2n² − n + 2.
(2)
2(100) − 10 + 2 = 192✓✓ (2)

TOTAL: 14 marks