Question

Joe's manager asked him to stack 3 cases of soda cans in a pyramid such that there's 1 can at the top layer, 2 cans at the next layer, 3 cans at the next layer, 4 cans at the next layer, and so on... How many cans could Joe put at the bottom layer for this pyramid?

A. 5 cans
B. 6 cans
C. 7 cans
D. 8 cans

Answer 1

Joe can put 6 cans at the bottom layer of the pyramid.

Step-by-step explanation:

To find the number of cans that Joe can put at the bottom layer of the pyramid, we need to add up the number of cans in each layer. The number of cans in each layer forms an arithmetic sequence with a common difference of 1. So, the first layer has 1 can, the second layer has 2 cans, the third layer has 3 cans, and so on.

To find the total number of cans, we need to sum the terms of the arithmetic sequence. The formula for the sum of an arithmetic sequence is S = n/2(2a + (n-1)d), where S is the sum, n is the number of terms, a is the first term, and d is the common difference.

In this case, a = 1 and d = 1, since the first term is 1 and the common difference is 1. Let's find the sum for n = 3:

S = 3/2(2(1) + (3-1)(1))

S = 3/2(2 + 2)

S = 3/2(4)

S = 3/2 * 4

S = 12/2

S = 6

Therefore, Joe can put 6 cans at the bottom layer of the pyramid.