Let's analyze the pattern in the sequence provided:

3, 5, 9, 15, 23, ...

Looking at the differences between consecutive numbers:

• 5 - 3 = 2
• 9 - 5 = 4
• 15 - 9 = 6
• 23 - 15 = 8

The differences are increasing by 2 each time. Based on this pattern, the next difference should be 10.

Adding this difference to the last number:

• 23 + 10 = 33

Therefore, the next number in the pattern is 33, which corresponds to option E.

Would you like further clarification or have any questions about this solution? Here are a few more related questions:

1. How can we apply this pattern to other number sequences?
2. What if the differences weren't increasing by 2 each time—how would the approach change?
3. Can you find other patterns where differences between numbers follow a similar progression?
4. How can patterns in sequences be used to predict future values in real-world situations?
5. What are other common types of number patterns we encounter in mathematics?

Tip: When working with number patterns, always start by analyzing the differences or ratios between numbers to identify the underlying rule.