The question asks for the next three terms in the arithmetic sequence given as $9, 19, 29, 39, \ldots$.

Step-by-Step Solution:

1. Identify the common difference:
   Subtract any two consecutive terms.
   $19 - 9 = 10, \quad 29 - 19 = 10, \quad 39 - 29 = 10$
   Thus, the common difference is $10$.

2. Generate the next terms:
   Start from the last given term, $39$, and add the common difference repeatedly.

   \text{Next term: } 49 + 10 = 59 \text{Next term: } 59 + 10 = 69$$

3. The next three terms are: $49, 59, 69$.

Correct Option:

The correct answer is the fourth option: 49, 59, 69.

Would you like more detailed explanations or have any follow-up questions?

Related Questions:

1. What are the properties of an arithmetic sequence?
2. How do you find the $n$-th term of an arithmetic sequence?
3. Can arithmetic sequences have negative differences? Provide an example.
4. What distinguishes an arithmetic sequence from a geometric sequence?
5. How do you find the sum of the first $n$ terms of an arithmetic sequence?

Tip: Always verify the common difference in an arithmetic sequence before predicting future terms!