what is geometric sequence

A geometric sequence, also known as a geometric progression, 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, every term in a geometric sequence is multiplied by a constant which results in its next term. For example, the sequence 2, 6, 18, 54, ... is a geometric progression with common ratio 3, while 10, 5, 2.5, 1.25, ... is a geometric sequence with common ratio 1/2. Geometric sequences can be represented by the formula an = a1 * r^(n-1), where a1 is the first term, r is the common ratio, and n is the position of the term. To check whether a given sequence is geometric, one simply checks whether successive entries in the sequence all have the same ratio. The behavior of a geometric sequence depends on the common ratio, and whether it is greater than, less than, or equal to 1.