Which of the following best describes this sequence? \( \{135,45,15,5, \ldots\} \) An arithmetic sequence with a common ratio of \( \frac{1}{3} \). An arithmetic sequence with a common difference of 3 . A geometric sequence with a common difference of 3 . A geometric sequence with a common ratio of \( \frac{1}{3} \).

This sequence \( \{135, 45, 15, 5, \ldots\} \) is characterized by each term being multiplied by \( \frac{1}{3} \) to get the next term. For instance, \( 135 \times \frac{1}{3} = 45 \), \( 45 \times \frac{1}{3} = 15 \), and so forth. This indicates that it is a geometric sequence, as it consistently involves multiplication rather than addition or subtraction. In the realm of mathematical sequences, geometric sequences can be found in various real-world scenarios, such as in finance while calculating compound interest or in nature when observing patterns like population growth. Understanding these sequences, especially how ratios work, can be key in making predictions based on current trends.