A paper manufacturer buys a machine for exist120000 During t

A paper manufacturer buys a machine for exist120,000. During the next 5 years, it will depreciate at a rate of 30% per year. (In other words, at the end of each year the depreciated value will be 70% of what it was at the beginning of the year). Find the formula for the nth term of a geometric sequence that gives the value of the machine t full years after it was purchased.

Solution

initial value = $ 120,000

depreciates at the rate of 30%

2nd year value would be 120,000 - .30(120,000) = 120,000 ( 1- .30)

= 120,000 ( .7 )

3rd year it would be

120,000 (.7)^2 .. and so on

hence , geometric sequence formula is

An = 120,000 (0.7 ) ^n-1