If you pile oranges in a pyramid with 1 orange in the first layer, 4 in the second layer, 9 in the third layer , and 16 in the fourth layer.

Question

How many oranges will you need to make a pile with ten layers?

Answer 1

1, 4, 9, 16, 25, 36, 49, 64, 81, and 100 for the number of oranges from the first to the 10th layer.

 

You can get the answer by adding all of the numbers:

 

181 + 113 + 61 + 25 + 5 = 294 + 86 + 5 = 385.

 

 

Also, you could sum up the first n squares using the formula, 

 

S_n = n(n+1)(2n +1)/6

 

 

S₁₀ = 10(11)(21)/6 = 385