The sequence 5, 9, 17, 34 appears to be increasing at a rate where each term grows by approximately twice the difference of the previous increase.

Let's break it down:

• From 5 to 9, the difference is $9 - 5 = 4$.
• From 9 to 17, the difference is $17 - 9 = 8$.
• From 17 to 34, the difference is $34 - 17 = 17$.

Looking at the pattern:

• The differences are doubling (4, 8, and 17 is roughly double 8). So, the next difference might be $34$.

Thus, the next number in the sequence would be: $34 + 34 = 68.$

Therefore, the next number is 68.

Would you like to explore the sequence further or ask any questions?

Here are 5 related questions:

1. Can you find a general formula for this sequence?
2. What is the sum of the first 5 terms of this sequence?
3. How does this sequence relate to geometric sequences?
4. What if the difference triples instead of doubles?
5. How do you classify this type of sequence?

Tip: Look for patterns in the differences between terms when solving sequences.