Sequences
Presentation
•
Mathematics
•
6th - 8th Grade
•
Easy
Jan Steele
Used 4+ times
FREE Resource
11 Slides • 21 Questions
1
Sequences
2
What do I already know about Sequences?
Do I know any 'famous' number sequences?
Do they have special names?
How are the terms generated? Are they related to each other or to a special rule?
3
Multiple Select
The Triangular numbers are
1, 8, 27, 64, ......
1, 3, 6, 10, .......
2, 4, 6, 8, .......
1, 3, 5, 7, ....
1, 4, 9, 16,......
4
Multiple Select
The cube numbers are
1, 1, 2, 3, 5,.....
2, 4, 6, 8,......
1, 8, 27, 64,.....
1, 3, 5, 7,......
1, 3, 6, 10,.....
5
Multiple Select
The even numbers are
1, 3, 6, 10,...
1, 8, 27, 64,....
1, 4, 9, 16,....
2, 4, 6, 8,.....
1, 1, 2, 3, 5,....
6
Multiple Select
The odd numbers are
1, 3, 5, 7,.....
1, 1, 2, 3, 5,..
2, 4, 6, 8,....
1, 8, 27, 64,.....
1, 4, 9, 16,....
7
Multiple Select
The Fibonacci numbers are
1, 3, 6, 10,....
1, 8, 27, 64,......
2, 4, 6, 8,.....
1, 1, 2, 3, 5,......
1, 4, 9, 16
8
Open Ended
For the odd/even numbers, how is the sequence generated?
9
Open Ended
For the square numbers, how is the sequence generated?
10
Open Ended
Why are the numbers called ‘square’?
Could we represent the sequence in diagram form?
11
Open Ended
Triangular numbers, how is the sequence generated?
12
Open Ended
Why are the numbers called ‘cube’? Could we represent
the sequence in diagram form?
13
Open Ended
Fibonacci numbers, how is the sequence generated?
14
Open Ended
Is there a link between the term number and the terms of the
sequence? Careful. This one is tricky!
15
Open Ended
Is this a term-to-term rule? How could I work out the
100th term without writing out all 100 terms?
16
Open Ended
Is there a rule relating to the position of the term I
am looking for?
17
Types of Sequences
Arithmetic
Geometric
Neither
18
Types of Sequences (cont.)
An arithmetic sequence changes by adding or subtracting the same amount each time,
eg 3, 6, 9, 12, …. or 12, 10, 8, 6, ….
A geometric sequence changes by multiplying or dividing by the same amount each time,
eg 3, 6, 12, 24, …. or 100, 50, 25, 12.5, …
Sequences can be either arithmetic or geometric or neither.
19
So, what types were the sequences above?
Arithmetic – odd numbers, even numbers
Geometric - none of these
Neither - Fibonacci, triangular, square, cube
20
Term-to-Term & Position-to-Term Rules
Sequences can be defined using a term-to-term rule.
Each term is generated from the previous term using the rule.
What term-to-term rules might we use?
21
Open Ended
Generate at most 2 sequences of your own and state whether they are:
- Arithmetic
OR
-Geometric
22
Position - to - Term
A position-to-term rule describes each term of the sequence in relation to its position in the sequence.
This rule can be given in words or in algebra.
The position is usually denoted by the letter n so if we want the 10th term, we would put n = 10 into a formula.
23
For example 2, 4, 6, 8, 10, .… is obtained by doubling the term number
Term 1 = 2×1
Term 2 = 2×2
Term 3 = 2×3
Term 4 = 2×4 etc.
So a formula for the nth term would be 2×n or 2n
24
Using a table:
Position number 1 2 3 4 5
Term 2 4 6 8 10
25
Open Ended
1. What would be the 17th term of this sequence?
2. Is 103 in this sequence?
3. What is the position of the term 84?
26
The answers are:
- 17th term is 2×17 = 34
- 103 is not in the sequence as all the numbers are even.
The term number for 103 would have to be 103 ÷ 2 = 51.5 and this is not possible as position numbers have to be whole numbers
- 84 ÷ 2 = 42 so it is the 42nd term.
27
Open Ended
Write out the position-to-term rule, in words, for each of the following sequences listed below:
a) 5, 10, 15, 20,....
b) 13, 26, 39, 52,....
c) 2, 5, 8, 11,.....
For each sequence above, answer the following questions:
i) What is the 50th term?
ii) Is the number 60 in the sequence? How do you know?
iii) Can the rule be written in algebra?
28
The answers are:
a) 5, 10, 15, 20, …. ‘multiply position number by 5’ 5n
b) 13, 26, 39, 52, .… ‘multiply position number by 13’ 13n
c) 2, 5, 8, 11, …. ‘multiply position number by 3 then subtract 1’ 3n−1
29
Open Ended
Write the first four terms for the sequence below:
'An arithmetic sequence with a difference of two between the terms'
30
Open Ended
Write the first four terms for the sequence below:
'A geometric sequence in which the next term is double the previous term'
31
Open Ended
Write the first four terms for the sequence below:
'An arithmetic sequence involving fractions'
32
Open Ended
Write the first four terms for the sequence below:
'A geometric sequence involving division'
Sequences
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