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A11 nth terms and sequences in context

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The following sequence of patterns is made from L-shaped tiles:

Number of Tiles 4 8 12

The number of tiles in each pattern forms a sequence.

How many tiles will be needed for the next pattern?

16

We add on four tiles each time. This is a term-to-term rule.

Sequences from practical contexts

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A possible justification of this rule is that each shape has four ‘arms’ each increasing by one tile in the next arrangement.

The pattern give us multiples of 4:

1 lot of 4 2 lots of 4 3 lots of 4 4 lots of 4

The nth term is 4 × n or 4n.

Justification: This follows because the 10th term would be 10 lots of 4.

Sequences from practical contexts

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Garden Tiles 1

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The number of blue tiles in a pattern form the sequence 8, 13, 18, 23, ...

Patternnumber 1

Number ofblue tiles 8

2

13

3

18

The rule for the nth term of this sequence isT(n) = 5n + 3

Justification: Each time we add another yellow tile we add 5 blue tiles. The +3 comes from the 3 tiles at the start of each pattern.

Garden Tiles 2

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Dotty pattern 1

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Leapfrog investigation