Derive and use the finite geometric series formula to solve problems such as mortgage-payment models.
Write a finite geometric series model for repeated depreciation or discount and identify the first term, common ratio, and number of terms
Problem
Write a finite geometric series for the total of \(5\) year-end values of equipment initially worth \(1000\) that loses \(20\%\) each year.
Big Picture
What this problem is really about
Convert a percent loss into the fraction that remains, since repeated depreciation multiplies by the retention factor rather than by the loss rate. Timing determines the first exponent: if the requested list begins after one period, the initial time-zero value is not included. Count the requested period-end values inclusively to set the final exponent and number of terms.
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