Arithmetic and Geometric Progressions
An arithmetic progression is a sequence of numbers where the difference between the consecutive terms is constant. For example the sequence 0, 5, 10, 15, 20, 25 ... is an arithmetic progression with difference of 5 between consecutive terms.
A geometric progression is a sequence of numbers where each term after the first is calculated by multiplying the previous common ratio. For example the sequence 2, 4, 6, 8, 10 ... is a geometric geometric with common ratio 2.
Progressions are quite common in every day life, for example if you are saving money in equal amounts each week, then your total savings is an arithmetic progression with the common difference being the amount you are saving each week. A common use of geometric progressions is the drepreciation of an asset such as a car, if the car depreciates at a rate of 15% per year, then the value of the car after each year can be calculated through the use of a geometric progression with an inital value of the purchase price of the car and the common ratio being 0.15.