finding position-to-term rules find position-to-term rules for these sequences:
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![Page 1: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/1.jpg)
Finding position-to-term rules
![Page 2: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/2.jpg)
Finding position-to-term rules
For the sequence: 5 9 13 17 21 ….
![Page 3: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/3.jpg)
Finding position-to-term rules
For the sequence: 5 9 13 17 21 ….
Position number 1 2 3 4 5
Term 5 9 13 17 21
![Page 4: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/4.jpg)
Finding position-to-term rules
For the sequence: 5 9 13 17 21 ….
Position number 1 2 3 4 5
Term 5 9 13 17 21
The rule for this sequence is
X 4
![Page 5: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/5.jpg)
Finding position-to-term rules
For the sequence: 5 9 13 17 21 ….
Position number 1 2 3 4 5 4 8 12 16 20
Term 5 9 13 17 21
The rule for this sequence is
X 4
![Page 6: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/6.jpg)
Finding position-to-term rules
For the sequence: 5 9 13 17 21 ….
Position number 1 2 3 4 5 4 8 12 16 20
Term 5 9 13 17 21
The rule for this sequence is
X 4 + 1
![Page 7: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/7.jpg)
Finding position-to-term rules
For the sequence: 5 9 13 17 21 ….
Position number 1 2 3 4 5
x 4 +1
Term 5 9 13 17 21
![Page 8: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/8.jpg)
Finding position-to-term rules
For the sequence: 5 9 13 17 21 ….
Position number 1 2 3 4 5
x 4 +1
Term 5 9 13 17 21
The formula for the nth term of the sequence is:
tn = 4n + 1
![Page 9: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/9.jpg)
Find position-to-term rules for these sequences:
1) 4 7 10 13 …..
2) 4 9 14 19 …..
3) 2 12 22 32 …..
4) -13 -6 1 8 …..
5) 3 2 1 0 …..
![Page 10: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/10.jpg)
Squares investigation
![Page 11: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/11.jpg)
Squares investigation
Imagine a 3 x 3 square:
![Page 12: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/12.jpg)
Squares investigation
Imagine a 3 x 3 square:
Colour the outside red:
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Squares investigation
Imagine a 3 x 3 square:
Colour the outside red:
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Squares investigation
How many of the small squares have
0 red sides? 1 red side? 2 red sides? 3 red sides? 4 red sides?
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Squares investigation
Now change the size of the starting square to
2 x 2 ? 4 x 4 ? etc…
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Squares investigation
How many of the small squares now have
0 red sides? 1 red side? 2 red sides? 3 red sides? 4 red sides?
INVESTIGATE!
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Generalising from Diagrams
8 by 8
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Generalising from Diagrams
20 by 20
50 by 50
100 by 100
n by n
2 red sides = ?
1 red side = ?
0 red sides = ?
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Generalising from Diagram
20 by 30
50 by 40
90 by 50
a by b
2 red sides = ?
1 red side = ?
0 red sides = ?
![Page 20: Finding position-to-term rules Find position-to-term rules for these sequences:](https://reader036.vdocuments.us/reader036/viewer/2022082611/56649e465503460f94b3b35b/html5/thumbnails/20.jpg)
Squares investigation
Put your results into a table! (If you need to)
Work methodically!
Spot patterns!
Try to find some general rules!