To predict the next number in the sequence 2, 5, 10, 17, 26 using inductive reasoning, let's examine the pattern of differences between consecutive terms.

1. $5 - 2 = 3$
2. $10 - 5 = 5$
3. $17 - 10 = 7$
4. $26 - 17 = 9$

The differences between consecutive terms are increasing by 2 each time (3, 5, 7, 9). Based on this pattern, the next difference should be $9 + 2 = 11$.

Therefore, the next number in the sequence would be: $26 + 11 = 37$

Thus, the next number is 37.

Would you like further details or have any questions?

Here are 5 related questions you could explore:

1. What if the differences were increasing by a different number?
2. Can you find a formula for the $n$-th term in the sequence?
3. How would you approach finding patterns in a more complex sequence?
4. How does inductive reasoning differ from deductive reasoning in math?
5. Can this sequence represent a real-world scenario?

Tip: In sequences, always check for both arithmetic and geometric progressions to uncover hidden patterns.