Download Introduction to linear sequences

Introduction to linear sequences
1. For each of the following sequences, find:
 the next two terms,
 the rule to find the next term (term-term).
a) 4, 7, 10, 13, 16 …
b) 36, 41, 46, 51, 56 …
c) 18, 16, 14, 12, 10 …
d) 27, 17, 7, -3, -13 …
e) 1.3, 1.6, 1.9, 2.2, 2.5 …
f) 3½, 3¾, 4, 4¼, 4½ …
g) -2, -6, -10, -14, -18 …
h) -13, -10, -7, -4, -1 …
2. For these first terms and term-term rules, find:
 the first five terms,
 a quick way to find the tenth term,
 the tenth term.
a) 1st term: 41
term-term rule: +3
d) 1st term: -9
term-term rule: +4
b) 1st term: 57
term-term rule: -4
e) 1st term: 2
term-term rule: + ¼
c) 1st term: 10
term-term rule: -5
f) 1st term: 6
term-term rule: -0.2
3. 5, 9, 13, 17, 21 …
Example:
5, 7, 9, 11, 13 …
5, 7, 9, 11, 13, 15, 17
term-term rule: +2
Example:
7, 13, 19, 25, 31
10th term = 7 + 9 x 6
= 61
Explain your answers without
calculating next terms.
Is the number 52 in this sequence?
4. 36, 42, 48, 54, 60 …
Explain your answers without
calculating next terms.
a. Is the number 83 in this sequence?
b. Is the number 82 in the sequence?
c. Is the number 84 in the sequence?
Extension: non-linear sequences
1, 4, 9, 16, 25 …
a. Is the number 49 in this sequence?
b. Is the number 99 in this sequence?
c. What is the name of this sequence?
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Introduction to linear sequences
Answers
1.
2.
a)
4, 7, 10, 13, 16, 19, 21
term-term rule: +3
e)
1.3, 1.6, 1.9, 2.2, 2.5, 2.8, 3.1
term-term rule: +0.3
b)
36, 41, 46, 51, 56, 61, 66
term-term rule: +5
f)
3½, 3¾, 4, 4¼, 4½, 4¾, 5
term-term rule: +¼
c)
18, 16, 14, 12, 10, 8, 6
term-term rule: -2
g)
-2, -6, -10, -14, -18, -22, -26
term-term rule: -4
d)
27, 17, 7, -3, -13, -23, -33
term-term rule: -10
h)
-13, -10, -7, -4, -1, 2, 5
term-term rule: +3
a)
41, 44, 47, 50, 53
10th term = 41 + 9x3
= 68
d)
-9, -5, -1, 3, 7
10th term = -9 + 9x4
= 27
b)
57, 53, 49, 45, 41
10th term = 57 – 9x4
= 21
e)
2, 2¼, 2½, 2¾, 3, 3¼
10th term = 2 + 9x¼
= 4¼
c)
10, 5, 0, -5, -10
10th term = 10 – 9x5
= -35
f)
6, 5.8, 5.6, 5.4, 5.2
10th term = 6 – 9x0.2
= 4.2
3.
52 is not in the sequence. The sequence only has even numbers.
4.
a)
83 is not in the sequence. The sequence only has even numbers.
b)
82 is not in the sequence. The sequence only has multiples of six.
c)
84 is in the sequence. It is a multiple of six.
Extension: non-linear sequences
1, 4, 9, 16, 25 …
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a)
The number 49 is in the sequence.
b)
The number 99 is not in the sequence.
c)
This is the sequence of square numbers.
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