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Sequences
A set of numbers where each number can
be obtained from the previous number
according to some rule is called a
sequence
The most simplest sequence is the set
of natural numbers
1, 2, 3, 4, 5, 6, 7, 8, 9, . . .
The terms of other sequences can be obtained
from the sequence of natural numbers
Consider the even numbers
rd 4th 5th 6th, … nth
1st1, 2nd
3
2, 3, 4, 5, 6, …
2,2, 4,
10, 12,
12,…… 2n
4, 6, 8, 10,
Can you describe how the even numbers
are obtained from the sequence of natural
numbers?
We can see that the even numbers can be
obtained by multiplying the natural numbers
by 2
The nth term is obtained by 2n
Consider the odd numbers
1st 1,2nd2, 3rd3, 44,th 55,th 6,
6th…
, … nth
1, 1, 3,3, 5,5, 7,7, 9,9, 11,
11, …
… 2n - 1
Can you describe how the odd numbers
are obtained from the sequence of natural
numbers?
We can see that the odd numbers can be
obtained by multiplying the natural numbers
by 2 and then subtracting 1
The nth term is obtained by 2n - 1
Write down the first 5 terms of the sequence
produced by multiplying the natural numbers
by 7 and subtracting 4
1,
2,
3,
7 - 4,
14 - 4,
21 - 4,
3,
10,
17,
4,
5, …
28 - 4 , 35 - 4, …
24,
31, …
What is the nth term of this sequence?
The nth term is given by 7n - 4
Describe the way that this sequence is
produced from the natural numbers:
5, 8, 11, 14, …
First number the terms of the sequence and
find the difference between each term
1st
2nd
3rd
4th
5,
8,
11,
14, …
+3
+3
+3
Because the difference is 3, this sequence
will be based on the 3 times table
1st
2nd
3rd
4th
nth
3
6
9
12
3n
5,
8,
11,
14, … 3n + 2
The sequence is produced by multiplying
the natural numbers by 3 and adding 2
What is the nth term of this sequence?
The nth term is given by 3n + 2
Find a rule for the nth term of this sequence:
-5, -1, 3 , 7, 11, …
First number the terms of the sequence and
find the difference between each term
1st
2nd
3rd
4th
5th
-5,
-1,
3,
7,
11, …
+4
+4
+4
+4
Because the difference is 4, this sequence
will be based on the 4 times table
1st
2nd
3rd
4th
5th
4
8
12
16
20
-5,
-1,
3,
7,
11, …
nth
4n
4n - 9
The sequence is produced by multiplying
the natural numbers by 4 and subtracting 9
What is the nth term of this sequence?
The nth term is given by 4n - 9
A bead maker has red beads and blues
beads and will make necklaces with the
following pattern:
Find a rule for how many blue beads
will be used with n red beads.
How many blue beads will be needed
when there are 100 red beads?
The number of red beads is in the sequence
of natural numbers
Red beads 1
2
3
Blue beads
6
8
+2
10
+2
The sequence is based on the 2 times table
Red beads
Blue beads
1
2
3
2
4
6
6
8
10
Red beads: 1
2
3
n
2
4
6
2n
Blue beads: 6
8
10
2n + 4
Number of blue beads is 2 X number of red
beads + 4
Number of blue beads = 2n + 4
Number of blue beads = 2 X 100 + 4 = 204