A geometric sequence is a sequence where the ratio r of any term to its preceding term is a constant other than 0. This ratio is called the common ratio. In the following geometric sequence, the first term is 3, and the common ratio is 2.
Each term of a geometric sequence is multiplied by the common ratio r to get the next term. Like any other sequence, the first term of a geometric sequence is denoted by a1, the second a2, and so on.
Therefore, geometric sequences have the following form.
This is very similar to the rate of change of an exponential function. The number 1.5 would, in that case, be the constant multiplier. In fact, when graphing a geometric sequence in a coordinate plane, it resembles the graph of an exponential function.
A vet gives medicine to an axolotl for a week. The first dose is 32 mg, and every day it's cut in half. List the doses in a sequence and graph it in a coordinate plane.