Question

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?

Answer 1

Each level has seven blocks more than the level above it, so summing up the amount of blocks per level:\[5+(5+7)+(5+7+7)+...\]Which, can be equivalently expressed by\[(5+0*7)+(5+1*7)+(5+2*7)+...+(5+24*7)\]Which, can be equivalently expressed by\[25*5+(0+1+2+...+24)*7\]The summation in the parenthesis can be condensed as follows, by recognizing that paring up each term with the one symmetrically at the other side always adds up to 24, plus the additional odd term in the middle that needs to be added additionally:\[25*5+(12*24+12)*7\]Evaluate this in a calculator and you will get\[2225\]

Answer 2

OMG!!! i love you... i posted this question like 5 days in a row and you are the only person to answer or attempt.... :)

Answer 3

:D My pleasure!