Transcript SEQUENCES Learning Objectives

SEQUENCES
Learning Objectives
• Generate terms of a simple sequence, given
a rule, finding a term from the previous term
• Generate terms of a simple sequence, given
a rule, finding a term given its position in the
sequence
•To find the nth term of a linear sequence
Look at this sequence
Term
1
2
3
4
5
Sequence
4
7
10
13
16
What is the second term
of the sequence?
7
What is the fourth term
of the sequence?
13
Look at this sequence
Term
1
2
3
4
5
6
7
Sequence
4
7
10
13
16
19
22
3
3
3
3
What do you notice about the
numbers in the sequence?
3
Add 3
What is the sixth term?
19
What is the seventh term?
22
3
Look at this sequence
Term
1
2
3
4
5
Sequence
3
7
11
15
19
What is the second term
of the sequence?
7
What is the fourth term
of the sequence?
15
Look at this sequence
Term
1
2
3
4
5
6
7
Sequence
3
7
11
15
19
23
27
4
4
4
4
What do you notice about the
numbers in the sequence?
4
Add 4
What is the sixth term?
23
What is the seventh term?
27
4
This method of finding the next term in
the sequence by adding the difference is
known as the term to term method
Term
1
2
3
4
5
6
7
Sequence
3
7
11
15
19
23
27
To get the next number in the
sequence you simply add the
difference!
4
4
We need a method of finding any term in
the sequence by using a rule to work out
any number by using it’s position in the
sequence.
This method is known as the position to
term method.
1
2
3
4
5
10
3
7
11
15
19
39
If we want to know the 10th number we use
a rule.
Look at this sequence
Term
1
2
3
4
5
Sequence
4
7
10
13
16
3
3
3
3
The pattern is add 3 each time, but what is
the rule?
The multiplier in the rule is always the
same as the number you add for the term
to term rule.
Look at this sequence
Term
1
2
3
4
5
Sequence
4
7
10
13
16
The multiplier in the rule is always the
same as the pattern number. When we
multiply the term number by 3 we do not
get the answer
2 x 3 is not 7
4 x 3 is not 13
This same sequence
Term
0
1
2
3
4
5
Sequence
1
4
7
10
13
16
3
3
3
3
3
To find the rule we look at the zero term,
the term BEFORE the sequence starts.
So the zero term is + 1
So the rule is: times by 3 then + 1 or 3n + 1
Finding the nth term
Term
0
1
2
3
4
5
4
7
10
13
16
So the rule is:
times by 3
then + 1
Sequence
1
3
3
3
3
3
The rule is: x 3 + 1 or 3n + 1
Finding the 10th term :
Term
0
1
2
3
4
5
x3 +1
3n + 1
Sequence
1
4
7
10
13
16
3
So the 10th term is:
3 x 10 + 1 = 31
When the zero term is negative
Term
0
1
2
3
4
5
-1 3
7
11
15
19
So the rule is:
times by 4
then - 1
Sequence
4
4
4
4
The rule is x 4 - 1 or 4n - 1
4
Finding the 10th term :
Term
0
1
2
3
4
5
x4 -1
Sequence
-1 3
7
11
15
19
4
So the 10th term is:
4 x 10 - 1 = 39
The End
Now it’s your turn…