Use inductive reasoning to predict the next number in 2, 5, 10, 17, 26, ?

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.

Discover how to use inductive reasoning to find the next number in the sequence 2, 5, 10, 17, 26. Learn about the arithmetic progression pattern and the increasing differences between terms. This step-by-step guide is perfect for students in Grades 6-8.

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