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In a geometric sequence, each term after the first is obtained by multiplying the previous one by a fixed, non-zero number known as the "common ratio." This ratio is a fundamental element that determines the sequence's progression. To find this common ratio, all you need to do is divide any term in the sequence by the previous term. In our exercise, the common ratio is identified by dividing the second term by the first term:

• Second Term: 135
• First Term: 405

Performing the division, we get:\[ r = \frac{135}{405} = \frac{1}{3}\]So, each term in the sequence is one third of the previous term, pointing to a decreasing sequence. Understanding the common ratio is essential, as it allows us to predict and extend the sequence.

Once the common ratio in a geometric sequence is known, calculating the subsequent terms becomes straightforward. This is done by multiplying the previous term in the sequence by the common ratio.To find the fourth term in our specific sequence, we start from the third term, which is 45. Using the common ratio we found earlier, \( r = \frac{1}{3} \), we multiply:\[ 45 \times \frac{1}{3} = 15\]Therefore, the fourth term in the sequence is 15. Each step of multiplying builds directly on the previous number, offering a simple yet powerful method to continue the sequence. Knowing how to find the fourth term solidifies understanding of the sequence's pattern, making it easier to predict further terms.

To determine the fifth term in the sequence, continue with the same process used for calculating the fourth term. You now start with the fourth term, which we've just found to be 15.Strike again with the common ratio by multiplying:\[ 15 \times \frac{1}{3} = 5\]This calculation shows us that the fifth term is 5. By repeatedly applying the common ratio, the geometric sequence unfolds in a predictable pattern. Knowing how to find terms like the fifth term enables us to extend sequences and understand the deeper structure connecting each number. Such skills are highly useful in both academic settings and real-world applications where sequence patterns appear.