# Machinery at a factory originally costing $50,000 depreciates $1800 the first year, $1750 the second year, $1700 the year etcWhat is the amount of depreciation during the fifth year? What is the...

Machinery at a factory originally costing $50,000 depreciates $1800 the first year, $1750 the second year, $1700 the year etc

What is the amount of depreciation during the fifth year?

What is the value of the machinery at the end of the fifth year?

Does this involve an arithmetic sequence or a geometric sequence?

Use the proper formulas where applicable. Show your work.

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### 1 Answer

Notice that each year machinery depreciates $50 less from the amount of depreciation of previous year, hence:

year 1 = $1800

year 2 = $1800 - $50 = $1750

year 3 = year 2 - $50 = (year 1 - $50) - $50 = year 1 - 2*$50 = $1700

year 5 = year 1 - 4*$50 = $1800 - $200 = $1600

Hence, the amount of depreciation during the fifth year is of $1600.

You need to evaluate the value of machinery at the end of the fifth year subtracting the amounts of depreciation of each year such that:

Cost after five years = $50,000 - ($1800 + $1750 + $1700 + $1650 + $1600) = $41,500

Notice that you may find the amount of depreciation during the fifth year using the formula involving an arithmetic sequence with common difference of $50.

**Hence, the amount of depreciation during the fifth year is of $1600, the cost of machinery after five years is of $41,500 and the problem involves an arithmetic sequence with common difference of $50.**