#### Linear number patterns - Arithmetic progression : answers.

1.1
Constant difference = d = 8 - 4 = 4 OR d = 12 - 8 = 4
1.2
16 + 4 = 20; 20 + 4 = 24; 24 + 4 = 28 The next three terms are 20; 24; 28.
1.3
a = first term = 4 and d = difference between consecutive terms = 8 - 4 = 12 - 8 = 4
T n = a + (n - 1)d = 4 + (n - 1) x 4 = 4n
The rule is the value of the nth term is equal to four times the number of the term.
1.4
The twentieth term = T 20 = 4 x term number = 4 x 20 = 80
2.1
Die constant difference = d = 5 - 2 = 3 and the next three terms are 11 + 3; 14 + 3 and 17 + 3
i.e. 14, 17 and 20
2.2
The general term of the pattern = T n = a + (n - 1)d = 2 + (n - 1) x 3 = 3n - 1
2.3
T n = 3 x 33 - 1 = 99 - 1 = 98
2.4
T 9 = 3 x 9 - 1 = 26
3.1
7; 12; 17; 22; . . .    a = 7;   d = 12 - 7 = 5 and T n = a + (n - 1)d = 7 + (n - 1) x 5 = 5n + 2
3.2
13; 20; 27; 34; . . .    a = 13;   d = 20 - 13 = 7 and T n = a + (n - 1)d = 13 + (n - 1) x 7 = 7n + 6
3.3
51; 62; 73; . . .    a = 51;    d = 62 - 51 = 11 and T n = a + (n - 1)d = 51 + (n - 1) x 11 = 11n + 40
3.4
64; 61; 58; 55; . . .    a = 64;    d = 61 - 64 = - 3
T n = a + (n - 1)d = 64 + (n - 1) x (-3) = -3n + 67 = 67 - 3n
3.5
81; 74; 67; . . .    a = 81;    d = 74 - 81 = - 7
T n = a + (n - 1)d = 81 + (n - 1) x (-7) = -7n + 88 = 88 - 7n
3.6
11; 8; 5; . . .   a = 11;    d = 8 - 11 = - 3
T n = a + (n - 1)d = 11 + (n - 1) x (-3) = -3n + 14 = 14 - 3n
3.7
12; 8; 4; . . .   a = 12;    d = 8 - 12 = - 4
T n = a + (n - 1)d = 12 + (n - 1) x (-4) = -4n + 16 = 16 - 4n
3.8
-13; -20; -27; -34; . . .   a = -13;   d = -7;   T n = -7n - 6
3.9
-21; -26; -31; . . .   a = -21;   d = -5;   T n = -5n - 16
3.10
-11; -8; -5; . . .   a = -11;   d = 3;   T n = 3n - 14
3.11
-31; -28; -25; . . .   a = -31;   d = 3;   T n = 3n - 34
3.12
-11; -5; 1; . . .   a = -11;   d = 6;   T n = 6n - 17
2
4
6
8
2
2
2
2
2n
3.13
--- ;
--- ;
--- ;
--- ;  · · ·
a = --- ;    d = ---      T n = --- + (n - 1)---   =   -------
5
5
5
5
5
5
5
5
5
2
4
6
8
2
2
2
2
2n
3.14
--- ;
--- ;
--- ;
--- ;  · · ·
a = --- ;    d = ---      T n = --- + (n - 1)---   =   -------
7
7
7
7
7
7
7
7
7
2
4

8
2
2
2
2
2n
3.15
--- ;
--- ;
2 ;
--- ;  · · ·
a = --- ;    d = ---      T n = --- + (n - 1)---   =   -------
3
3

3
3
3
3
3
3
3
1
1

3
3
3
3
3n
3.16
--- ;
1 --- ;
2 ---;
3  · ·
a = --- ;    d = ---      T n = --- + (n - 1)---   =   -------
4
2
4

4
4
4
4
4
-1
1

5
-1
2
-1
2
2n
3.17
--- ;
--- ;
1;
--- ;  · ·
a = --- ;    d = ---      T n = --- + (n - 1)---   =   ------- - 1
3
3

3
3
3
3
3
3
-18

-10
-6
-18
4
-18
4
4n
22
3.18
------ ;
-2 ;
------;
--- ;  ·
a = ----- ;    d = ---      T n = ------ + (n - 1)---   =   ------- - ------
7

7
7
7
7
7
7
7
7

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