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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.

Respuesta :

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 [tex]1,3,5,...[/tex]

This forms an arithmetic progression with common difference as [tex]3-1=5-3=2[/tex]

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

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

Here, [tex]S_n[/tex] denotes sum of n terms.

Put [tex]a=1,d=2,n=12[/tex]

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

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