A construction crane sells for 400000 if purchased new After

A construction crane sells for $400000 if purchased new. After that, the value decreases by 30% each year. We can use a geometric sequence to find the value of the crane at the end of each year. If we let a0 represent the value when it is purchased, then

a. a1 is value after 1 year, a2 is the value after 2 years, and so on to a5.

b. what is the common ratio

c.write the sequence from part a using recursive formula an=

Solution

a) ao = $400000 , a1 = 400000( 1- 30/100) = $280000

a2 = 280000(1-30/100) = $196000

a5 = 400000(1-3/100)(1-3/100)(1-3/100)(1-3/100)(1-3/100) = $67228

b) common ratio = 280000/400000 = 0.7

c) a_n = a_n-1*(0.7)