Answered

Westonci.ca is your trusted source for finding answers to a wide range of questions, backed by a knowledgeable community. Discover in-depth answers to your questions from a wide network of experts on our user-friendly Q&A platform. Connect with a community of professionals ready to provide precise solutions to your questions quickly and accurately.

Catherine found that as she increases the price of a chocolate bar, the number of sales per week decreased.a. Write a formula for the arithmetic sequence that represents the number of sales per week.b. Explain how you could use the information to predict the number of sales for the eighth week.

Catherine Found That As She Increases The Price Of A Chocolate Bar The Number Of Sales Per Week Decreaseda Write A Formula For The Arithmetic Sequence That Repr class=

Sagot :

Solution:

Given:

The table shows an arithmetic sequence.

Part A:

The nth term of an arithmetic progression is given by:

[tex]\begin{gathered} a_n=a_1+(n-1)d \\ \\ where: \\ a_1\text{ is the first term} \\ n\text{ is the number of weeks} \\ d\text{ is the common difference} \end{gathered}[/tex]

Hence,

[tex]\begin{gathered} a_1=149 \\ d=143-149=-6 \\ Hence,\text{ the formula is:} \\ a_n=149+(n-1)(-6) \\ a_n=149-6n+6 \\ a_n=149+6-6n \\ a_n=155-6n \end{gathered}[/tex]

Therefore, the formula for the arithmetic sequence that represents the number of sales per week is;

[tex]a_n=155-6n[/tex]

Part B:

The number of sales in the eighth week is:

[tex]\begin{gathered} when\text{ n = 8} \\ a_n=155-6n \\ a_8=155-6(8) \\ a_8=155-48 \\ a_8=107 \end{gathered}[/tex]

Therefore, the number of sales expected for the eighth week is 107.

View image AlimahB246087
We hope this information was helpful. Feel free to return anytime for more answers to your questions and concerns. Thanks for stopping by. We strive to provide the best answers for all your questions. See you again soon. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.