MATHEMATICS
MORE EXERCISES

Question  1
sequence : 8 ; 13; 20; 29; . . .
1.1  Write down the following two
terms.                                            [ A 1.1 ]
1.2  Determine the general term,
Tn.                                                 [ A 1.2 ]
1.3  Calculate the value of the
twenty first term, T21                     [ A 1.3 ]
1.4  Which term is equal to 148?         [ A 1.4 ]

Question  2
sequence : ─2 ; ─1; 4; 13; . . .
2.1  Write down the following two
numbers.                                    [ A 2.1 ]
2.2  Determine the general term,
Tn.                                              [ A 2.2 ]
2.3  Calculate the value of the
fifteenth term, T15.                     [ A 2.3 ]

2.4  Which term is equal
to 494?                                      [ A 2.4 ]

Question  3
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,
Tn.                                                   [ A 3.2 ]
3.3  Calculate the value of the
nineth term,   T9.                             [ A 3.3 ]
3.4  Determine the value of n
if Tn = 355.                                      [ A 3.4 ]

Question  4
12;   7;   ─2;   ─15;   . . .

4.1  Write down the following two
numbers.                                     [ A 4.1 ]
4.2  Determine the general term,
Tn.                                               [ A 4.2 ]
4.3  Calculate the value of the
eleventh term,   T11.                    [ A 4.3 ]
4.4  Determine the value of n
if Tn = −617.                                [ A 4.4 ]

Question  5
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. ]

Question  6
1;   p;   21;   q; . . .

The second differences are equal to 4.
Calculate the values of p and q.
[ A 6. ]

Question  7
The sequence    ─ 2;   x;   y;   . . .   is a
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. ]

Question  8
4;    9;    x;    37;   . . .

8.1  Calculate x.                               [ A 8.1 ]
8.2  Determine the nth term.            [ A 8.2 ]

Paper 1, November 2010

Question  9
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 ]

Question  10
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 ]

Question  11
The general term of a quadratic
sequence is given by
Tn = 3(n + 2)2 ─ 4   Determine the first
first difference. the constant second
difference and the first term.            [ A 11. ]

Question  12
The pattern  −7;  −8;  −11;  −16;
12.1  Determine the nth term
Tn.                                           [ A 12.1 ]

12.2  Determine the seventeenth
term, T17.                                [ A 12.2 ]

12.3  Determine the value of n
if Tn < −313.                            [ A 12.3 ]

12.4  Between which TWO terms of
will there be a difference
of −43?                                    [ A 12.4 ]

Question  13
The general term of a quadratic number
pattern is given by −n2 + 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 T16.
[ 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
number pattern.                         [ A 13.5 ]

13.6  Which TWO consecutive terms
have a first difference of −5?
[ A 13.6 ]

Question  14
The general term of a quadratic number
pattern is given by 3n2 − 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 T7.
[ 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
have a first difference of 125?
[ A 14.4 ]