Complete the Number Sequence: Finding the Pattern Starting with 5, 7

Complete the following sequence:

$5,7\ldots$

To solve this problem, we'll identify whether the sequence follows a recognizable pattern. The sequence so far is $5, 7$.

Let's determine whether it follows an arithmetic sequence:

• First Term ($a_1$) = 5
• Second Term ($a_2$) = 7
• The Common Difference ($d$) = $7 - 5 = 2$

Assuming a consistent common difference, the sequence appears to be an arithmetic sequence increasing every term by 2.

Let's calculate the next few terms:

• Third Term ($a_3$) = $7 + 2 = 9$
• Fourth Term ($a_4$) = $9 + 2 = 11$
• Fifth Term ($a_5$) = $11 + 2 = 13$

Thus, the full sequence is: $5, 7, 9, 11, 13$.

A review of the multiple-choice options shows that the correct answer is given by choice 1: $5, 7, 9, 11, 13$.

Therefore, the complete sequence is $5, 7, 9, 11, 13$.