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.
(a) For a straight-line depreciation: (3000-200)/4=700.
3000-700, 3000-700*2, 3000-700*3, ...
The solution provides detailed explanation how to find arithmetic sequence for depreciation.