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  • The students in a school are having a cup stacking contest. John has a pyramid 9 layers high. How many cups will he need to add to his pyramid to increase the number of layers to 12?

The students in a school are having a cup stacking contest. John has a pyramid 9 layers high. How many cups will he need to add to his pyramid to increase the number of layers to 12?

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total;number;of;cups;at;level ,L=L\* total;number;of;cups; for; all; levels ;from ;1 ;to; L=1+2+3+...+L\* Rightarrow fracL( L + 1)2\* So,;the;number;of;cups;needed;to;increase;the;number\*of;layers;to ;12;from ;9 ;is:\*Rightarrow frac12(12+1)2 - frac9(9+1)2=78-45=33\* So,;he;need;33;more;cups ;to;add ;to ;his; pyramid; to; increase ;the ;number; of; layers; to; 12

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Deependra Verma

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