Find the Missing Term in Sequence: 5, ?, 45, 135

To find the 2nd element of the sequence $5, \text{ ?}, 45, 135, \text{ ?}, \text{ ?}$, we'll first work to identify any patterns in the sequence.

Let's start by examining the given terms:

• The first term is $5$.
• The third term is $45$.
• The fourth term is $135$.

Notice that:

• The third term ($45$) is exactly $9$ times the first term ($5$).
• The fourth term ($135$) is exactly $3$ times the third term ($45$).

From the above points, it suggests a regular multiplication pattern. Let's test if the factor between each term is consistent.

Given the third term can be expressed as $5 \times 9 = 45$ and the fourth term as $45 \times 3 = 135$, it implies:

The missing terms might follow a similar multiplication pattern. To find the 2nd term, let's assume the sequence between the 1st and 3rd terms is a continuous multiplication sequence.

Assume the sequence's pattern alternates between multiplication by $3$ and multiplication by another constant. Therefore:

• The second term is $5 \times 3 = 15$.
• Continuing with the geometric pattern: $15 \times 3 = 45$, confirming the third term.

This confirms the consistent alternating multiplication pattern exists, matching the sequence's terms so far. Therefore, the second term in the sequence is indeed $\mathbf{15}$.

The solution to the problem is $15$.