Number patterns

#### Question 2

Here is a pattern of shapes made from matches.

Detailed description of diagram

a |
Write down a sequence of 6 numbers giving the number of matches in each of these diagrams and the next two in the obvious sequence. |

b |
Give the rule for finding the next term in this pattern. |

#### Solution

How do you go from diagram 1 to diagram 2?

You add 3 matches in the manner shown.

How do you go from diagram 2 to diagram 3?

You add 3 matches.

This can be continued to produce each successive diagram.

a |
Term 1: 4 | Term 2: 7 | Term 3: 10 | ||

Term 4: 13 | Term 5: 16 | Term 6: 19 | |||

b |
Add 3 |

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