Finding position-to-term rules

Finding position-to-term rules

For the sequence: 5 9 13 17 21 ….

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

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

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

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

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

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

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 …..

Squares investigation

Squares investigation

Imagine a 3 x 3 square:

Squares investigation

Imagine a 3 x 3 square:

Colour the outside red:

Squares investigation

Imagine a 3 x 3 square:

Colour the outside red:

Squares investigation

How many of the small squares have

0 red sides? 1 red side? 2 red sides? 3 red sides? 4 red sides?

Squares investigation

Now change the size of the starting square to

2 x 2 ? 4 x 4 ? etc…

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!

Generalising from Diagrams

8 by 8

Generalising from Diagrams

20 by 20

50 by 50

100 by 100

n by n

2 red sides = ?

1 red side = ?

0 red sides = ?

Generalising from Diagram

20 by 30

50 by 40

90 by 50

a by b

2 red sides = ?

1 red side = ?

0 red sides = ?

Squares investigation

Put your results into a table! (If you need to)

Work methodically!

Spot patterns!

Try to find some general rules!