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A child is creating a pyramid with building blocks. The top three levels include 5 blocks, 12 blocks, and 19 blocks. How many blocks would be needed for a pyramid 25 levels tall? Use complete sentences to explain how a sum of an arithmetic series was applied.

Mathematics
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[5 + (7*0)] + [5 + (7*1)] + [5 + (7*2)] + ... + [5 + (7*24)] = (25)(5) + 7(1 + 2 + 3 + ... + 24) = 125 + 7[(24)(25)]/2
That's a lot of blocks for one child! :-)
The key is that the sum of 1 + 2 + 3 + ... + (n-1) + n = n(n+1)/2

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