What comes next in the sequence: 2, 6, 18, 54, ...?

The sequence 2, 6, 18, 54, ... follows a clear mathematical pattern where each term is generated by multiplying the previous term by a constant value. In this particular series, if you divide any term by its preceding term, you consistently arrive at the number 3. For example, 6 divided by 2 is 3, 18 divided by 6 is 3, and 54 divided by 18 is also 3. This constant multiplier is known as the common ratio, and it defines the nature of this type of numerical progression.

Recognizing this pattern, to determine the next number in the sequence, we simply apply the same rule. Multiplying the last given term, 54, by the common ratio of 3 yields 162. Therefore, 162 is the correct continuation of the series. This kind of sequence is formally known as a geometric progression, a fundamental concept in mathematics.

Geometric progressions are not just abstract puzzles; they appear in many real-world scenarios. They are used to model phenomena exhibiting exponential growth or decay, such as compound interest in finance, population growth, radioactive decay, or even the spread of certain rumors. Understanding these sequences provides a foundational insight into how quantities can change rapidly over time through constant proportional increases or decreases, demonstrating the power of simple mathematical rules to describe complex processes.