Question

A grocery store owner is planning a display by stacking cans of soup in a pyramid. The top row of the stack will have 1 can, the row underneath it will have 3 cans, the row underneath it will have 5 cans, and so on. If the owner wants the display to have a total of 12 rows, then how many cans will he need? Show your work. Explain how you know your answer is correct.

Answer 1

Answer:

144 cans

Step-by-step explanation:

Number of cans in the top row = 1

Number of cans in the second row = 3

Number of cans in the third row = 5

Here, the sequence obtained is $1,3,5,...$

This forms an arithmetic progression with common difference as $3-1=5-3=2$

Let d denotes the common difference and n denotes number of terms.

$S_n=\frac{n}{2}[2a+(n-1)d]$

Here, $S_n$ denotes sum of n terms.

Put $a=1,d=2,n=12$

$S_{12}=\frac{12}{2}[2(1)+(12-1)2]\\=6[2+(11)2]\\=6(2+22)\\=6(24)\\=144$