Answer
The value at the end of the sixth year is
$a_{6} \approx 23530$
Work Step by Step
Since the machine loses $30\%$ of its value each year, it retains $70\%$ of its value
Its value at the end of each of the following years is $70\%$ of the previous year’s value. These values form a geometric sequence, with $r = 0.7, a=200.000$
The value at the end of the sixth year is
$a_{6}=200.000(0.7)^{7-1} \approx 23530$
