the manager of a grovery store asks a store clerk to rearrange a display of canned vegtables in a triangular pyramid. Assume all cans are thr same size and shape.

Question

in the first pyramid their is 1 can in the base, second pyramid has 3 cans in the base and 3rd pyramid shown has 6 cans in the base.

A) if the clerk has 100 cans to use, how many of those can are needed to create the tallest complete pyramid shape?

B) how many can make up the bottom level of the pyramid in part A

c) how many levels is the pyramid in part A

For this question i have no idea where to start or if theirs a formula i can use. thank you for your help

Answer 1

the number of cans on each layer is a triangular number.
So, you need the sum of such numbers.
you could start here:

https://en.wikipedia.org/wiki/Tetrahedral_number