word problem

Question

Griffin used 14 block to build three-layer pyramid. How many blocks would he need to build a six-layer pyramid? How many blocks would he need for the bottom layer of a nine-layer pyramid?

Answer 1

the top layer is 1 block (1x1).

The second layer is 2x2 = 4 blocks.

The third layer is 3x3 = 9 blocks.

Add them together, and you have 14 blocks.

 

The formula for n layers is:

 

n

∑    i², which comes out to n(n+1)(2n+1)/6.

i=1

 

For a 6-layer period, plug 6 in place of n in the above formula.

 

The nth layer has n² blocks.  For the second question, plug 9 in place of n.