Given a pattern of groups of asterisks below diagram 1=6 diagram 2=12 diagram 3=20 diagram 4=30. Determine the general of this sequence?

Question

How many asterisks are there in diagram 10?

Comments

We don't have the pattern of asterisks!

Answer 1

Diagram 1 (6)

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Diagram 2 (12)

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Diagram 3 (20)

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Diagram 4 (30)

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The general pattern is n(n+1) where n is the number of asterisk pairs on the last row and n-1 is the diagram number.

So, Diagram 10 has 11 pairs of asterisks, so the total number is 11*12=132.