There are many uses of geometric sequences in everyday life, but one of the most common is in calculating interest earned. Mathematicians calculate a term in the series by multiplying the initial value in the sequence by the rate raised to the power of one less than the term number. The sequence allows a borrower to know the amount his bank expects him to pay back using simple interest.
In a geometric sequence, a term is determined by multiplying the previous term by the rate, explains to MathIsFun.com. One example of a geometric series, where r=2 is 4, 8, 16, 32, 64, 128, 256... If the rate is less than 1, but greater than zero, the number grows smaller with each term, as in 1, 1/2, 1/4, 1/8, 1/16, 1/32… where r=1/2. The only limitation on r is that it cannot equal zero.
Given the rate of travel, it is possible to apply this formula to determine the number of miles a vehicle travels in a given amount of time, and to calculate the distance at any time along the trip.
Physicists use geometric progressions to calculate the amount of radioactive material left after any given number of half-lives of the material. During each half-life, the material decays by 50 percent.