Complete the Number Sequence Starting with 1, 3: Find the Pattern

To solve this problem, we need to identify the pattern in the sequence provided, which initially lists the numbers $1$ and $3$.

First, observe the given numbers: $1$ and $3$.

The difference between the first term $1$ and the second term $3$ is:
$3 - 1 = 2$.

This suggests a common difference of $2$, implying that the sequence is likely an arithmetic sequence where each term increases by $2$.

We can use this observation to predict the next terms in the sequence:

• Starting with $1$, add the common difference $2$:
  $1 + 2 = 3$.
• From $3$, add the common difference $2$:
  $3 + 2 = 5$.
• Continuing this pattern, from $5$, add $2$:
  $5 + 2 = 7$.
• And from $7$, add the common difference $2$:
  $7 + 2 = 9$.

Thus, the sequence can be extended as:
$1, 3, 5, 7, 9$.

From the possible choices, the correct sequence is represented by choice 4.

Therefore, the correct answer to the problem is $1, 3, 5, 7, 9$.