MATEMATICS
MORE EXERCISES
Linear patterns, linear sequence.

Question  1
Study the linear pattern below.
Calculate the next two terms
of the pattern, i.e. the fourth and
fifth terms and the formula
for the general tern, Tn :
1.1    8;   13;   18;   . . .                     [ A 1.1 ]
1.2    38;   53;   68;   . . .                   [ A 1.2 ]
1.3    −23;   −15;   −7;   . . .                 [ A 1.3 ]
1.4    54;   41;   28;   .. .                    [ A 1.4 ]
1.5    −7;   −16;   −25;   .. .                  [ A 1.5 ]

Question  2
Study the following number pattern   :
7;   16;   25;   . . .

2.1  Say what kind of a pattern it
is. Give a reason.                      [ A 2.1 ]

2.2  Calculate the value of
2.2.1  T11                                            [ A 2.2.1 ]
2.2.2  n if Tn   =   124                        [ A 2.2.2 ]

Question  3
Consider the following number pattern   :
28;   35;   42;   . . .

3.1  What kind of pattern is it?
Give a reason.                            [ A 3.1 ]

3.2  Calculate the value of
3.2.1  T18                                            [ A 3.2.1 ]
3.2.2  n if Tn   =   203                        [ A 3.2.2 ]

Question  4
Consider the following number pattern   :
−134;  −161;  −188;   . . .

4.1  What kind of pattern is it?
Give a reason.                            [ A 4.1 ]

4.2  Calculate the value of
4.2.1  T9                                               [ A 4.2.1 ]
4.2.2  n if Tn   =  −404                         [ A 4.2.2 ]

Question  5
Given the linear pattern  :
87;   72;   57;   . . .
5.1  Calculate the value of T4       [ A 5.1 ]
5.2  Calculate the value of the
first seven terms.                       [ A 5.2 ]
5.3  What is the number and value of
the last positive term?              [ A 5.3 ]
5.4  Give the number and value of the
first negative term,                   [ A 5.4 ]
5.5  Calculate the value of
n if Tn > 0                                  [ A 5.5 ]
5.6  Calculate the value of
n if Tn < 0                                  [ A 5.6 ]

Question  6
Given the linear number pattern   :
18;   27;   36;   . . .
6.1  Calculate the formula for the
general term, Tn                        [ A 6.1 ]
6.2  Calculate the value of the
23rd term.                                   [ A 6.2 ]
6.3  Calculate the number of the term
which has a value of 288.        [ A 6.3 ]
6.4  Which term is the last term
smaller than 165?                     [ A 6.4 ]
6.5  Which term is the first term
greater than 380?                      [ A 6.5 ]

Question  7
Given the following linear number pattern   :
53;   48;   43;   . . .
7.1  Calculate the value of T7           [ A 7.1 ]
7.2  Calculate the value of n
if Tn = −27.                                     [ A 7.2 ]
7.3  Which term is the last term
with a positive value?               [ A 7.3 ]
7.4  Which term is the first
nagative term?                            [ A 7.4 ]

Question  8
Consider the following linear
pattern    :  63;   55;   47;   . . .
8.1  Determine the formula for the
general term, Tn.                         [ A 8.1 ]
8.2  Calculate the value of T7.          [ A 8.2 ]
8.3  Calculate the number of the
term which has a value of −25.     [ A 8.3 ]
8.4  Which term is the last
positive term?                              [ A 8.4 ]

Question  9
Consider the following linear number
pattern    :  −63;   −56;   −49;   . . .
9.1  Determine the formula for the
general term, Tn.                         [ A 9.1 ]
9.2  Which term is the first
positive term?.                             [ A 9.2 ]
9.3  Calculate the value of T18.
[ A 9.3 ]
9.4  Determine which term has
a value of 35                                 [ A 9.4 ]
9.5  Which term is the first term
greater than 110?                        [ A 9.5 ]
9.6  Which term is the last term
smaller than 180?                        [ A 9.6 ]

Question  10
Consider the linear number pattern   :
87;   78;   69;   . . .
10.1  Determine the value
of T13                                            [ A 10.1 ]
10.2  Which term has a value
of 15?                                            [ A 10.2 ]
10.3  Which term is the last term
greater than −60?                       [ A 10.3 ]
10.4  Which term is the first term
smaller than −94?                       [ A 10.4 ]
10.5  Which term is the first
negative term?                           [ A 10.5 ]

Question  11
In a linear number pattern
T10 =   44 and T19 =   80.
Calculate the first three terms.     [ A 11. ]

Question  12
T9 =   32 and T14 =   47 are two
terms in the same linear number
pattern. Calculate the
pattern, i.e. calculate the first
three terms of the pattern.             [ A 12. ]

Question  13
T5 =  5 and T12 =  −9 are two
terms in the same linear number
pattern. Calculate the
pattern, i.e. calculate the first
three terms of the pattern.            [ A 13. ]

Question  14
T6 =  −26 and T15 =  −53 are two
terms in the same linear number
pattern. Calculate the
pattern, i.e. calculate the first
three terms of the pattern.           [ A 14. ]

Question  15
T6 =   27 and T11 =   47 are two
terms in the same linear number
pattern.
15.1  Calculate the value
of T15                                           [ A 15.1 ]
15.2  Calculate the value of n
if Tn = 87.                                    [ A 15.2 ]

Question  16
In a linear number pattern
T9 is 12 greater than T5 and T24 =   74.
Determine the pattern.                     [ A 16. ]

Question  17
In a linear number pattern
T21 is 30 greater than T6 and
T13 =   33.
17.1  Determine the value
of T10.                                         [ A 17.1 ]
17.2  Which term has a value
of 67?                                          [ A 17.2 ]

Question  18
x − 2;   x + 2;  en 2x − 1  are the
firse three terms of a linear
number pattern.
18.1  Calculate the value of x          [ A 18.1 ]
18.2  Calculate the value of
the nineth term.                       [ A 18.2 ]

Question  19
7x − 4;   5x + 5 en   4x + 6   are the
first three terms of a linear
number pattern.
19.1  Calculate the pattern.             [ A 19.1 ]
19.2  Determine the value of
the sixth term.                          [ A 19.2 ]
19.3  Calculate the vale of n so that
Tn < 2.                                         [ A 19.3 ]

Question  20
2x − 2;   3x en   5x − 3   are the
first three tems of a linear
number pattern.
20.1  Calculate the pattern.               [ A 20.1 ]
20.2  Determine the value of T8       [ A 20.2 ]
20.3  Which term is the first term
having a value greater 100?    [ A 20.3 ]

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