Question

Catherine found that as she increases the price of a chocolate bar, the number of sales per week decreased. Week Number of Sales 1 149 2 143 3 137 4 131 5 125 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.

Answer 1

A) Tn =149+(n-1)-6

B) 107

Explanation:

1)149

2) 143

3) 137

4) 131

5)125

There is a decrease in price of chocolate bar each week. The decrease is in arithmetic progression.

For arithmetic progression,

Tn = a+(n-1)d

A)Formula for the arithmetic sequence that represents the number of sales per week

Where a = the starting price =149

n = number of weeks

d = difference between following week and the previous week =143-149=137-143=-6

Tn = value of sales in n weeks

Tn = a+(n-1)d

Tn =149+(n-1)-6

B)number of sales for the eighth week,

n = number of weeks=8

d = difference between following week and the previous week =143-149=137-143=- 6

a = the starting price =149

Tn = value of sales in eighth week

Tn = 149+(8-1)-6

= 149+(7×-6)

=149+-42=149-42

=107

To confirm

Week 5 = 125

Week 6 = 125-6=119

Week 7 = 119-6=113

Week 8 = 113-6=107