A dress is listed at $75. At the end of each week the price is reduced by $2.

(a) What is the price of the dress after 8 weeks?(b) After how many weeks will the dress be less than $50?

Answer

This problem describes an arithmetic sequence. The dress initially costs *a*_{1} = 75. Each week the price is reduced by $2, so *d* = -2. After *n* weeks the price of the dress will be

*a*_{n} = 75 + (*n* – 1)(-2).

(a) After 8 weeks the price of the dress is

*a*_{8} = 75 + (7)(-2) = 61.

The dress will be $61.

(b) We want to find the first *n* for which *a*_{n}<50.

75 + (*n* – 1)(-2) < 50

75 – 2*n* + 2 < 50

27 < 2*n*

13.5 < *n*

After 14 weeks the dress will be less than $50. We could confirm this answer by calculating *a*_{13} = 51 and *a*_{14} = 49.