Complete the Sequence: Finding Next Terms After 111, 113, 115

The sequence provided starts with the numbers $111, 113, 115$. To determine the continuation, we begin by calculating the difference between each pair of consecutive numbers.

Step 1: Calculate the difference between $113$ and $111$:

$113 - 111 = 2$.

Step 2: Calculate the difference between $115$ and $113$:

$115 - 113 = 2$.

We observe that each successive number in the sequence increases by $2$. This confirms that the sequence is an arithmetic sequence with a common difference of $2$.

Step 3: Continue the sequence by adding $2$ to the last number:

The next number after $115$ is $115 + 2 = 117$.

The number after $117$ is $117 + 2 = 119$.

The number after $119$ is $119 + 2 = 121$.

The number after $121$ is $121 + 2 = 123$.

Thus, the sequence $111, 113, 115, 117, 119, 121, 123$ is an arithmetic sequence with a common difference of $2$.

Comparing the sequence $117, 119, 121, 123$ to the choices, we find that the matching option is:

$117, 119, 121, 123$

Therefore, the correct answer is:

$117, 119, 121, 123$