a piece of machinery depreciates $6000 the first year, $5700 the second year, and $5400 the third year. if…

a piece of machinery depreciates $6000 the first year, $5700 the second year, and $5400 the third year. if the rate of depreciation is constant, what is the amount of depreciation of the piece of machinery in the sixth year? a $18,500 b $4500 c $36,500 d $4800

a piece of machinery depreciates $6000 the first year, $5700 the second year, and $5400 the third year. if the rate of depreciation is constant, what is the amount of depreciation of the piece of machinery in the sixth year? a $18,500 b $4500 c $36,500 d $4800

Answer

Explanation:

Step1: Identify the sequence type

The depreciation amounts are $6000, $5700, $5400,... This is an arithmetic sequence where the first term (a_1 = 6000) and the common difference (d) is (5700 - 6000=- 300) (or (5400 - 5700=-300)).

Step2: Use the arithmetic sequence formula

The formula for the (n)-th term of an arithmetic sequence is (a_n=a_1+(n - 1)d). We need to find the 6th term, so (n = 6), (a_1=6000), (d=- 300).

Substitute the values into the formula: (a_6=6000+(6 - 1)\times(-300)) (a_6=6000+5\times(-300)) (a_6=6000 - 1500) (a_6 = 4500)

Answer:

B. $4500