Question

Help me please I am so lost!!!

A square pyramid can be constructed by stacking equal-sized cubes on top of each other in squares until you have 1 cube forming the top layer. From the top down, the number of cubes in each layer will be 1, 4, 9, 16, 25, and so on. If a pyramid has 100 levels, how many cubes will the base consist of?
A.100
B.1,000
C.10,000
D.100,000

Answer 1

Can you tell what the number of cubes in each layer are?

Answer 2

Do you see the relationship between the levels?

1-1^2
2-2^2
5-5^2

Answer 3

i cant tell any relationship or any thing all i know is that each of those numbers increase by two or basically the numbers increase by odd numbers starting at 3

Answer 4

So you can count it like that and go 36.. 49.. etc.

but it's much easier if you realize that it's just the blocks squared.

the 10th block = 10 * 10

Answer 5

Look at the number of each layer compared tot he number of cubes in the layer:

1 - 1
2 - 4
3 - 9
4 - 16
5 - 25
6 - 36
7 - 49

What do you do to each number of the layer to get the number of cubes in the layer?
Specifically, what operation do you to do each layer number to get the number of cubes in that layer?

Answer 6

1 - 1 = 1^2
2 - 4 = 2^2
3 - 9 = 3^2
4 - 16 = 4^2
5 - 25 = 5^2
6 - 36 = 6^2
7 - 49 = 7^2

Notice that the number of cubes in each layer is the square of the number of the layer.