Question

A supermarket display consists of boxes of cereal. The bottom row has 42 boxes. Each row has eight fewer boxes than the row below it. The display has six rows. (a) Write and use a function to determine how many boxes are in the top row. Show your work.(b) Use the appropriate formula to determine the number of boxes in the entire display. Show your work

Answer 1

(a) 2 boxes

(b) 132 boxes

Explanation:

We can write a function based on the following:

`a_n=a_1+d\cdot(n-1)`

(a) It would be an arithmetic sequence, we replace each value and it would be as follows:

`\begin{gathered} a_6=42+-8\cdot(6-1) \\ a_6=42-8\cdot5 \\ a_6=42-40 \\ a_6=2 \end{gathered}`

To calculate the number of boxes in the entire display, we follow the following formula:

`\begin{gathered} s=(n)/(2)\cdot(2\cdot a_1+(n-1)\cdot d) \\ \text{ in this case would be:} \\ s=(6)/(2)\cdot(2\cdot42+(6-1)\cdot-8) \\ s=3\cdot(84-40) \\ s=3\cdot44 \\ s=132 \end{gathered}`