Question 26704: A very bored grocer was stacking oranges one day. She decided to stack them in a triangular pyramid. There was one orange in the top layer, three oranges in the second layer, six oranges in the third layer, and so on. Each layer except the top formed an equilateral triangle. How many oranges woluld it take her to build a pyramid 50 layers high?
Answer by venugopalramana(3286)   (Show Source):
You can put this solution on YOUR website! A very bored grocer was stacking oranges one day. She decided to stack them in a triangular pyramid. There was one orange in the top layer, three oranges in the second layer, six oranges in the third layer, and so on. Each layer except the top formed an equilateral triangle. How many oranges woluld it take her to build a pyramid 50 layers high?
LAYER NUMBER........ORANGES
I ....................1
II....=3+2+1=.........6
III...=6+5+4=.........15
IV....=9+8+7=.........24
.......
SO TOTAL ORANGES ARE 1+(6+15+24+.......49 TERMS)
SEQUENCE IN BRACKETS IS A.P WITH A=6,D=9 AND N=49
HENCE SUM =SN=(N/2)(2A+(N-1)D)=(49/2)(2*6+(49-1)*9)=10878
SO NUMBER OF ORANGES REQD =1+10878=10879
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