Question

Haley likes to help her father at his grocery store she just finished setting up a display of Soup cans 12 rows high in the shape of a triangle there are 4 cans in the top row each of the rows below has 2 cans added at each end so there are 8 cans in the next row 12 cans in the next row and so one how many cans are in the bottom row?

Answer 1

Since the first row has 4 cans, the second has 8 and the third has 12, we can write the following sequence:

`4,8,12,\ldots`

notice that the common difference in this sequences is d = 4. Then, we can use the formula to find the expression of the sequence:

`\begin{gathered} a_n=a_1+(n-1)d \\ a_1=4 \\ d=4 \\ \Rightarrow a_n=4+(n-1)(4)=4+4n-4=4n \\ a_n=4n \end{gathered}`

then, on the bottom row, we have that n = 12, then:

`a_(12)=4(12)=48`

therefore, there are 48 cans in the bottom row