A geometric sequence is a list 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 number is multiplied by 3 to get the next one. This pattern continues indefinitely, making geometric sequences useful in various fields like finance and science. These sequences can grow or shrink rapidly, depending on the common ratio. If the ratio is greater than 1, the sequence increases, while a ratio between 0 and 1 causes it to decrease. Understanding geometric sequences helps in solving problems related to exponential growth, such as population growth or compound interest.