Depreciation For tax purposes, businesses frequently depreciate equipment. Two methods of depreciation ...

Depreciation For tax purposes, businesses frequently depreciate equipment. Two methods of depreciation are straight-line depreciation and sum-of-the-years’-digits. Suppose that a college student buys a $3000 computer to start a business that provides Internet services. This student estimates the life of the computer at 4 years, after which its value will be $200. The difference between $3000 and $200, or $2800, may be deducted from the student’s taxable income over a 4-year period. In straight-line depreciation, equal portions of $2800 are deducted each year over the 4 years. The sum-of-the years’- digits method calculates depreciation differently. For a computer having a useful life of 4 years, the sum of the years is computed by 1 + 2 + 3 + 4 + 10. With this method,4/10 of $2800 is deducted the first year,3/10 the second year, and so on, until 1/10 is deducted the fourth year. Both depreciation methods yield a total deduction of $2800 over the 4 years. (Source: Sharp Electronics Corporation, Conquering the Sciences.) (a) Find an arithmetic sequence that gives the amount depreciated each year by each method. (b) Write a series whose sum is the amount depreciated over 4 years by each method.