what is a geometric sequence

A geometric sequence is a sequence of non-zero numbers where each term after the first is found by multiplying the previous one by a fixed, non-zero number called the common ratio. In other words, a geometric sequence is a sequence where the ratio of every two successive terms is a constant. The general form of a geometric sequence is a, ar, ar^2, ... where a is the first term and r is the common ratio of the sequence. The common ratio can be either a positive or a negative number. To check whether a given sequence is geometric, one simply checks whether successive entries in the sequence all have the same ratio. A finite geometric sequence is a geometric sequence that contains a finite number of terms, while an infinite geometric sequence is a geometric sequence that contains an infinite number of terms.