Download Integers 1a

Patterns & Sequences
Extra questions for before the assessment
Please try these questions.
(You’ll find the answers on the last three pages)
Key Skill 1: Find particular terms in a sequence
Find the next 5 terms in the following sequences:
(a)
2, 7, 12, 17, ___, ___, ___, ___, ___
(b)
1, 2, 4, 8, ___, ___, ___, ___, ___
(c)
32, 30, 28, 26, ___, ___, ___, ___, ___
(d)
1, 1, 2, 3, 5, 8, ___, ___, ___, ___, ___
(e)
55, 54, 52, 49, ___, ___, ___, ___, ___
(f)
1, 3, 6, 10, ___, ___, ___, ___, ___
Find the 9th term in the following sequences:
(g)
1, 4, 7, …
(h)
1, 10, 100, …
(i)
100, 95, 90, 85, …
(j)
1, 20, 39, …
(k)
2, 2.5, 3, 3.5, …
(l)
0.1, 0.01, 0.001, …
Key Skill 2: Find missing terms in a sequence
Find the unknown term in the following sequences:
(a)
4, 8, 12, a, 20, 24, …
(b)
40, 37, 34, 31, b, 25, 22, …
(c)
10, 21, 32, 43, 54, c, …
(d)
d, 19, 28, 37, 46, …
(e)
1.25, 1.75, 2.25, e, 3.25, …
(f)
1000, 990, 960, 910, 840, f, …
Key Skill 3: Determine the rule for a sequence
Find the rule for the following sequences:
(a)
8, 15, 22, 29, …
(b)
9, 17, 25, 33, 41, …
(c)
5, 10, 20, 40, 80, …
(d)
50, 41, 32, 23, 14, …
(e)
2700, 900, 300, 100, …
(f)
3, 30, 300, 3000, 30000, …
Key Skill 4: Given the rule for a sequence, and its first term, list the set of numbers generated
Continue the sequences below by 5 terms
Question
First term
Rule
(a)
6
+4
6,
(b)
4
+ 12
4,
(c)
16
÷2
16,
(d)
10
x3
10,
(e)
80
- 12
80,
(f)
2000
- 150
2000,
(g)
0.5
x5
Sequence
0.5,
Key Skill 5: Determine the formula for a sequence
Find the formula for each table below:
Formula
(a)
n
sequence
1
3
2
6
3
9
4
12
5
15
Formula
(b)
n
sequence
1
5
2
10
3
15
4
20
5
25
Formula
(c)
n
sequence
1
12
2
13
3
14
4
15
5
16
Formula
(d)
n
sequence
1
8
2
9
3
10
4
11
5
12
Formula
(e)
n
sequence
1
3
2
5
3
7
4
9
5
11
Formula
(f)
n
sequence
1
9
2
12
3
15
4
18
5
21
Formula
(g)
n
sequence
1
1
2
4
3
7
4
10
5
13
Answers
Key Skill 1
(a)
2, 7, 12, 17, 22, 27, 32, 37, 42
(b)
1, 2, 4, 8, 16, 32, 64, 128, 256
(c)
32, 30, 28, 26, 24, 22, 20, 18, 16
(d)
1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89
(e)
55, 54, 52, 49, 45, 40, 34, 27, 19
(f)
1, 3, 6, 10, 15, 21, 28, 36, 45
(g)
1, 4, 7, 10, 13, 16, 19, 22, 25, 28, 31, …
(h)
1, 10, 100, 1000, 10000, 100 000, 1 000 000, 10 000 000, 100 000 000, …
(i)
100, 95, 90, 85, 80, 75, 70, 65, 60, 55, 50, …
(j)
1, 20, 39, 58, 77, 96, 115, 134, 153, 172, …
(k)
2, 2.5, 3, 3.5, 4, 4.5, 5, 5.5, 6, 6.5, 7, 7.5, 8, 8.5, …
(l)
0.1, 0.01, 0.001, 0.0001, 0.00001, 0.000001, 0.0000001, 0.00000001, 0.000000001…
Key Skill 2
(a)
4, 8, 12, a, 20, 24, …
a = 16
(b)
40, 37, 34, 31, b, 25, 22, …
b = 28
(c)
10, 21, 32, 43, 54, c, …
c = 65
(d)
d, 19, 28, 37, 46, …
d = 10
(e)
1.25, 1.75, 2.25, e, 3.25, …
e = 2.75
(f)
1000, 990, 960, 910, 840, f, …
f = 750
Key Skill 3
(a)
8, 15, 22, 29, …
rule + 7
(b)
9, 17, 25, 33, 41, …
rule + 8
(c)
5, 10, 20, 40, 80, …
rule x 2
(d)
50, 41, 32, 23, 14, …
rule – 9
(e)
2700, 900, 300, 100, …
rule ÷ 3
(f)
3, 30, 300, 3000, 30000, …
rule x 10
Key Skill 4
Question
First term
Rule
(a)
6
+4
6, 10, 14, 18, 22, 26
(b)
4
+ 12
4, 16, 28, 40, 52, 64
(c)
16
÷2
16, 8, 4, 2, 1, 0.5
(d)
10
x3
10, 30, 90, 270, 810, 2430
(e)
80
- 12
80, 68, 56, 44, 32, 20
(f)
2000
- 150
2000, 1850, 1700, 1550, 1400, 1250
(g)
0.5
x5
Sequence
0.5, 2.5, 12.5, 62.5, 312.5, 1562.5
Key Skill 5
Formula
(a)
n
sequence
1
3
2
6
3
9
4
12
5
15
3 x n or 3n
Formula
(b)
n
sequence
1
5
2
10
3
15
4
20
5
25
5 x n or 5n
Formula
(c)
n
sequence
1
12
2
13
3
14
4
15
5
16
n + 11
Formula
(d)
n
sequence
1
8
2
9
3
10
4
11
5
12
n+7
Formula
(e)
n
sequence
1
3
2
5
3
7
4
9
5
11
2xn+1
or
2n + 1
or
3n + 6
Formula
(f)
n
sequence
1
9
2
12
3
15
4
18
5
21
3xn+6
Formula
(g)
n
sequence
1
1
2
4
3
7
4
10
5
13
3xn–2
or
3n - 2