A geometric sequence is a series of numbers where each term after the first is found by multiplying the previous term by a fixed, non-zero number called the common ratio. For example, in the sequence 2, 6, 18, 54, each term is multiplied by 3 to get the next term. Geometric sequences can be represented using the formula a_n = a_1 \times r^(n-1) , where a_n is the nth term, a_1 is the first term, r is the common ratio, and n is the term number. These sequences are commonly found in various fields, including finance and science.