in a store all the oranges are stacked in triangular pyramids, each layer of oranges is in the shape of an equilateral triangle and the top layer is an single orange. How many oranges are are in a stack ten layers high

Answer 1

the layers are triangular numbers:
1,3,6,10, ... n(n+1)/2

The pyramid is pyramidal numbers:
1=1
1+3=4
1+3+6=10
...
1+3+...+n(n+1)/2 = n(n+1)(n+2)/6

Now just plug in n=10