The given sequence of numbers is: 4, 9, 14, 19.

Step 1: Identify the pattern

Looking at the differences between consecutive numbers:

• $9 - 4 = 5$
• $14 - 9 = 5$
• $19 - 14 = 5$

The difference between consecutive terms is consistently $5$.

Step 2: Use inductive reasoning

Since the pattern involves adding 5 to each term, we can find the next two numbers by continuing this pattern:

• Next number: $19 + 5 = 24$
• Second next number: $24 + 5 = 29$

Conclusion

The next two numbers in the sequence are 24 and 29.

Would you like more details, or do you have any questions?

Here are 5 related questions to deepen your understanding:

1. What is inductive reasoning in mathematics, and how does it apply here?
2. Can this sequence be represented as a function of $n$?
3. What other types of number patterns exist in mathematics?
4. How can you find the $n$-th term in an arithmetic sequence?
5. What is the difference between inductive and deductive reasoning in solving patterns?

Tip: Arithmetic sequences are patterns where the difference between consecutive terms is constant.