A geometric sequence is a list of numbers that keep changing by a constant ratio; for example:<\/p>\n
3,6,12,24,48….<\/p>\n
In the above sequence, t3<\/sub>=12.<\/p>\n A perfect fit for geometric sequences is depreciation:<\/p>\n Question 1:<\/u><\/p>\n A car originally valued at $10,000 depreciates by 18% per year. Find its value at the end of 7 years.<\/strong><\/p>\n Solution:<\/p>\n The fact that it depreciates by 18% means that it retains 82% of its value annually<\/em>. The constant ratio is therefore 82%, or 0.82, as shown:<\/p>\n 10000, 10000(0.82), 10000(0.82)2<\/sup>, 10000(0.82)3<\/sup>….<\/p>\n 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<\/sup>, will be the value after seven years’ depreciation:<\/p>\n t8<\/sub>=10000(0.82)7<\/sup>=2492.85<\/p>\n Apparently, the car’s value after 7 years’ depreciation is $2492.85.<\/p>\n Source:<\/p>\n Travers, Kenneth J. et al. Using Advanced Algebra<\/u>. Toronto: Doubleday Canada, 1977.<\/p>\n