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.
