In Grade 10 and 11 you learnt about linear and quadratic number patterns. Linear
number patterns have a constant difference between consecutive terms while
quadratic number patterns have a constant second difference.
REVISION OF QUADRATIC NUMBER PATTERNS
In Grade 11 we dealt with quadratic number patterns having a general term of the
form 2 Tn = ++ an bn c .
EXAMPLE
Consider the following number pattern: 2 ; 3 ; 6 ;11; …
(a) Determine the nth term (general term) and hence the value of the 42nd term.
(b) Determine which term will equal 1091.
Solutions
(a)
2
2
42
22 3 1 2
1 3(1) 1 (1) ( 2) 2
2 3
T 23
T (42) 2(42) 3 1683
n
a ab abc
a b
b c
n n
= += ++=
∴ = ∴ + = ∴ + − =
∴ = − ∴ =
∴ = − +
∴ = − + =
(b) T 1091 n =
2
2
2 3 1091
2 1088 0
( 34)( 32) 0
34 or 32
But 32
34
The 34th term will equal 1091
∴ − + =
∴− − =
∴ − + =
∴ = = −
≠ −
∴ =
n n
n n
n n
n n
n
n
REVISION EXERCISE
1. Determine the general term for each number pattern below.
2 3 6 11
1 3 5
2 2
abc + +
3a b +
2a
(a) 2; 6 ; 14 ; 26 ; … (b) 4 ; 9;16 ; 25 ; … (c) 1; 3 ; 6 ;10 ; …
(d) −1; 0 ; 3 ; 8 ; … (e) −−− − 3 ; 6; 11; 18 ; … (f) 10 ; 6 ; 3 ;1; …
2
2. Consider the following number pattern: 1; 6 ;15 ; 28 ; …
(a) Determine the general term and hence the value of the 20th term.
(b) Determine which term will equal 3160.
3. Consider the following number pattern: −− − − 4 ; 10 ; 18 ; 28 ; ..