The given sequence is: 2, 6, 12, 20, 30, 42, ...

We can observe that the differences between consecutive terms are increasing:

- \(6 - 2 = 4\)
- \(12 - 6 = 6\)
- \(20 - 12 = 8\)
- \(30 - 20 = 10\)
- \(42 - 30 = 12\)

The differences between consecutive terms form an arithmetic sequence with a common difference of 2.

Thus, the next difference should be \(12 + 2 = 14\). Adding 14 to 42 gives us the next term: 

\[42 + 14 = 56\]

So, the next term in the sequence is **56**.

Would you like more details on the approach or any other questions? Here are some related questions to explore:

1. What is the general formula for this sequence?
2. How can you classify this sequence?
3. What is the sum of the first 10 terms of the sequence?
4. How would you extend this sequence to the 15th term?
5. Can you express the nth term of this sequence using a quadratic equation?

**Tip**: When terms in a sequence have changing differences, you can often spot patterns by analyzing the difference between consecutive terms.

Explore the sequence 2, 6, 12, 20, 30, 42 and learn how to find the next term using arithmetic differences. Understand key mathematical concepts such as quadratic sequences and their formulas. Perfect for students in Grades 8-10.

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