Study the following quadratic number
sequence : 8 ; 13; 20; 29; . . .
1.1 Write down the following two
terms.
[ A 1.1 ]
1.2 Determine the general term,
T
n.
[ A 1.2 ]
1.3 Calculate the value of the
twenty first term, T
21
[ A 1.3 ]
1.4 Which term is equal to 148?
[ A 1.4 ]
Study the following quadratic number
sequence : ─2 ; ─1; 4; 13; . . .
2.1 Write down the following two
numbers.
[ A 2.1 ]
2.2 Determine the general term,
T
n.
[ A 2.2 ]
2.3 Calculate the value of the
fifteenth term, T
15.
[ A 2.3 ]
2.4 Which term is equal
to 494?
[ A 2.4 ]
The following numbers form a quadratic
quadratic sequence : ─5; 5; 17; 31; . . .
3.1 Write down the following two
nubers.
[ A 3.1 ]
3.2 Determine the general term,
T
n.
[ A 3.2 ]
3.3 Calculate the value of the
nineth term, T
9.
[ A 3.3 ]
3.4 Determine the value of n
if T
n = 355.
[ A 3.4 ]
Given the quadratic sequence :
12; 7; ─2; ─15; . . .
4.1 Write down the following two
numbers.
[ A 4.1 ]
4.2 Determine the general term,
T
n.
[ A 4.2 ]
4.3 Calculate the value of the
eleventh term, T
11.
[ A 4.3 ]
4.4 Determine the value of n
if T
n = −617.
[ A 4.4 ]
The following numbers form a quadratic
sequence : x; y; 8; . . .
The second difference of the sequence
is 2 and the second first difference 6.
Determine x and y.
[ A 5. ]
Given the quadratic sequence :
1; p; 21; q; . . .
The second differences are equal to 4.
Calculate the values of p and q.
[ A 6. ]
The sequence ─ 2; x; y; . . . is a
quadratic sequence with a constant
second difference of 2. The difference
between the second term and the third
term is 7. Determine the values of x and y.
[ A 7. ]
Given the quadratic sequence
4; 9; x; 37; . . .
8.1 Calculate x.
[ A 8.1 ]
8.2 Determine the nth term.
[ A 8.2 ]
Department of Education, Grade 12,
Paper 1, November 2010
A quadratic sequence has a second term
equal to 0, a third term equal to 6
and a fifth term equal to 24.
9.1 Calculate the second difference.
[ A 9.1 ]
9.2 Determine the first term.
[ A 9.2 ]
Given the quadratic sequence
6; 7; 12; p; . . .
10.1 Calculate the value of p.
[ A 10.1 ]
10.2 Determine the nth term.
[ A 10.2 ]
10.3 The first difference between
two consecutive terms of the
sequence is 53. Calculate the
value of these two terms.
[ A 10.3 ]
The general term of a quadratic
sequence is given by
T
n = 3(n + 2)
2 ─ 4 Determine the first
first difference. the constant second
difference and the first term.
[ A 11. ]
The pattern −7; −8; −11; −16;
is a quadratic number pattern.
12.1 Determine the nth term
T
n.
[ A 12.1 ]
12.2 Determine the seventeenth
term, T
17.
[ A 12.2 ]
12.3 Determine the value of n
if T
n < −313.
[ A 12.3 ]
12.4 Between which TWO terms of
the quadratic number pattern
will there be a difference
of −43?
[ A 12.4 ]
The general term of a quadratic number
pattern is given by −n
2 + bn − 150 and the
first term of the first difference is 15.
13.1 Show that b = 18.
[ A 13.1 ]
13.2 Determine the value of T
16.
[ A 13.2 ]
13.3 Which term is equal
to −598?
[ A 13.3 ]
13.4 Which term is the first term
that is less than −270?
[ A 13.4 ]
13.5 Determine the general term
for the sequence of the first
difference of the quadratic
number pattern.
[ A 13.5 ]
13.6 Which TWO consecutive terms
in the quadratic number pattern
have a first difference of −5?
[ A 13.6 ]
The general term of a quadratic number
pattern is given by 3n
2 − 4n + c and the
first term of the patern is −14.
14.1 Show that c = −13.
[ A 14.1 ]
14.2 Determine the value of T
7.
[ A 14.2 ]
14.3 Which term is the first term
that has a value greater
than 300?
[ A 14.3 ]
14.4 Which TWO consecutive terms
in the quadratic number pattern
have a first difference of 125?
[ A 14.4 ]