Math: geometric sequences: depreciation

The tutor brings up a real-life application for geometric sequences.

A geometric sequence is a list of numbers that keep changing by a constant ratio; for example:

3,6,12,24,48….

In the above sequence, t3=12.

A perfect fit for geometric sequences is depreciation:

Question 1:

A car originally valued at $10,000 depreciates by 18% per year. Find its value at the end of 7 years.

Solution:

The fact that it depreciates by 18% means that it retains 82% of its value annually. The constant ratio is therefore 82%, or 0.82, as shown:

10000, 10000(0.82), 10000(0.82)2, 10000(0.82)3….

Note that the first term, 10,000, doesn’t include any depreciation; the second term is the result of the first year’s depreciation. Similarly, the eighth term, which will be 10000(0.82)7, will be the value after seven years’ depreciation:

t8=10000(0.82)7=2492.85

Apparently, the car’s value after 7 years’ depreciation is $2492.85.

Source:

Travers, Kenneth J. et al. Using Advanced Algebra. Toronto: Doubleday Canada, 1977.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.

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