Worksheet 3 Memo: Number Patterns
Grade 11 Mathematics
1.
Identify the type of pattern and give the next three terms:
a)
…
b)
12; 24; 48; 96…
linear; subtract
(R)
each term is multiplied by 2;
192; 384; 768
c)
1; 8; 27; 64 …
(R)
each term position is cubed to give the next term; 125; 216; 343.
d)
1
Quadratic
6
14
5
8
11
3
e)
g)
25
39
14
3
17
3
1; 4; 9; 16 ….
f)
76
3
11; 16; 21; 26…
each term position is squared
linear, add 5;
25; 36; 49
31; 36; 41
48; 16;
h)
…
5
2
6
1
-1
…
6
0
-1
5
-1
-1
3
-2
-1
0
-3
-1
0; 3; 8; 15…
each term position is squared and then 1 is subtracted: 24; 35; 48
j)
1; 10; 101; 1010…
(R)
(R)
3
Quadratic
(R)
20
3
Divide each previous term by 3 →
i)
56
(R)
each term has a zero added after 1, or a 1 added after a 0; 10101; 101010; 1010101
(R)
2.
a)
125; 119; 113; 107…
-6
-6
b)
…
-6
( )
c)
8
17
9
(R)
( )
30
13
4
47
d)
5
17
8
11
3
3
14
(R)
3
4
( )
e)
( )
…
( )
f)
4
7
12
3
5
19
(R)
7
2
2
g)
1
5
14
4
9
5
28
(R)
14
5
( )
(
h)
32
19
-13
6
-13
( )
-7
-13
)
(R)
i)
2
6
13
4
7
23
j)
10
3
1
4
5
3
3
1
a)
c)
(
(
-2
(
e)
(
g)
i)
(
(
b)
)
)
(
4.
d)
)
f)
)
)
)
(
(
)
)
j)
c)
( )
(
)
(
)
(
)
)
h)
b)
a)
-1
-2
( )
3.
4
(
(
(
)
)
)
(
)
(R)
d)
81 is part of the sequence.
5.
-9
-3
6
3
6
9
b)
(
)
6
a)
c)
( )
d)
6.
a)
Sum
( )
-3
2
5
11
9
4
24
13
41
17
4
4
(
62
21
4
)
87
25
4
b)
( )
c)
(
)
(
d)
)
e)
(
N/A
)(
)
(
)
(
)
7.
a)
6
11
18
5
7
27
9
2
38
11
2
51
13
2
2
66
15
2
b)
( )
c)
(
)
(
)
d)
e)
(
)(
√
)
√
( )(
)
( )
N/A
98 is not part of the sequence
8.
a)
2
a
21
a–2
32
21 – a
21 – a – (a – 2)
11
11 – (21 – a)
b
b -32
b – 32 – 11
Ignore this one for now.
AND
b)
2
11
9
21
10
1
32
11
1
44
12
1
57
13
1
71
14
1
86
15
1
c)
( )
d)
(
)
(
f)
)
√
e)
( )(
√
)
( )
(
)(
N/A
)
242 is a part of the sequence
N/A
9.
a)
2
It is the 16th term.
2
a
0
b
a–2
a–2–0
b–a
b – a – (a – 2)
AND
2
2
0
10
8
8
26
16
8
50
24
8
82
32
8
122
40
8
170
48
8
50 – b
50 – b – (b – a)
AND
b)
50
c)
( )
d)
(
)
(
f)
)
√
)
√(
e)
( )(
)
( )
(
)(
1001 is not part of the sequence.
)
N/A
10.
a)
120
136
16
146
10
-6
150
4
-6
148
-2
-6
140
-8
-6
126
-14
-6
b)
(
c)
d)
√
)
√(
( )(
( )
seconds
e)
)
)
(
)
(
( )
[(
(
)
)
make
( )
( )
The building is 98m high
( )
]
)
11.
a)
7776m
7676m
-100
7524m
-152
-52
7320m
-204
-52
7064m
-256
-52
6750m
-308
-52
b)
6396m
-360
-52
(
)
c)
√
e)
(
√
(
)(
)
)
seconds
√
d)
(
)
(
(
√
)
(
)(
)
)
from the surface
f)
if
N/A
because it reaches the surface at 16,93 seconds
Then
(
)
(
)
In other words, 64m above the surface (i.e. in the air) which is impossible
no the
pattern cannot continue once the submarine has reached the surface.
12.
a)
216
185
-31
a
a – 185
a – 185 – (-31)
b
b–a
b – a – (a – 185)
AND
…1
…2
Subs 1 into 2:
188
188 – b
188 – b – (b – a)
b)
216
185
-31
170
-15
16
171
188
1
17
16
16
( )
c)
3 months → 3 × 4 = 12 weeks
(
)
(
)
d)
√
( )(
√
)
( )
or
after 14 weeks Sally will receive R1000 or more.
13.
0
1
1
1
0
-1
2
1
1
3
1
0
5
2
1
8
3
1
13
5
2
no the Fibonacci sequence is not a second common differences pattern as there is no common
second difference.