Make your own Number Patterns

You can make your own number patterns using coins or matchsticks. Here is an example using coins:

Size=1 Size=2 Size=3 Size=4
1 Coin 6 Coins 15 Coins 28 Coins

How many coins would you need when Size=5 ?

Can you make a formula that will tell you how many coins are needed for any Size? For example Size=20? The formula may look something like

Coins = Size × Size + ...

 

(Note: There are lots of number patterns in Pascal's Triangle)

 

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