Comment
You should confirm that the formula works. Try calculating a couple of rows to see what you get.
Preliminary Calculations
P(n) = n * (n +1)(2n + 1) / 6 Let n = 1
P(1) = 1 * (1 +1)(2*1 + 1) / 6
p(1) = (1 * 2 + 3)/6
P(1) = 6/6
P(1) = 1
The tip of the pyramid has 1 orange. Now try n = 2.
P(2) = 2*(2 + 1)(2*2+1)/6
P(2) = 2(3)(5)/6
P(2) = 30 / 6
P(2) = 5
The reason you want to do this is to show what exactly you are finding. What you have discovered is that this formula totals the current layer and all the layers above it.
Note: It does not give you the number of oranges in the current layer. It gives you the total number of oranges in layers 6 5 4 3 2 1. It is very important to know what you are calculating.
Question
The total number of oranges in 6 layers is
P(6) = 6 ( 6 + 1) (2*6 + 1) /6 Cancel the 6s
P(6) = (7 ) (13)
P(6) = 91
C <<<< Answer.