What is the next term in the sequence: 0, 10, 24, 56, 112, ______ ?​

Let's analyze the given sequence: 0, 10, 24, 56, 112, ...

To find the pattern, observe the differences between consecutive terms:
- \( 10 - 0 = 10 \)
- \( 24 - 10 = 14 \)
- \( 56 - 24 = 32 \)
- \( 112 - 56 = 56 \)

Now, let's look at the differences of the differences:
- \( 14 - 10 = 4 \)
- \( 32 - 14 = 18 \)
- \( 56 - 32 = 24 \)

The second-order differences are increasing by 6: \( 18 - 4 = 14 \), and \( 24 - 18 = 6 \).

Assuming this pattern continues, the next difference of the differences should be \( 24 + 6 = 30 \).

Thus, the next first-order difference will be \( 56 + 30 = 86 \), and the next term in the sequence will be:
\[ 112 + 86 = 198 \]

So, the next term in the sequence is **198**.

Would you like more details on how to find sequences, or do you have any questions? Here are five related questions:

1. How do you calculate differences in a sequence?
2. What are second-order differences?
3. Can you explain how to predict the next term in any sequence?
4. What are arithmetic and geometric sequences?
5. How do polynomials relate to sequences?

**Tip**: Always check higher-order differences when dealing with non-linear sequences!

Discover the method to find the next term in the sequence 0, 10, 24, 56, 112, with a detailed explanation of second-order differences and pattern recognition. Learn key concepts such as difference sequences and second-order differences. Suitable for students in Grades 8-10.

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