Question (10 Marks):

Consider the following sequence:
2, 6, 12, 20, 30, 42, ...

1. Identify the pattern governing this sequence. (2 Marks)
2. Derive a formula for the $n$-th term of the sequence. (3 Marks)
3. Use the formula to calculate the 10th term in the sequence. (2 Marks)
4. Verify your result by finding the difference between consecutive terms, showing the relationship between the terms. (3 Marks)

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Here are 5 related questions to expand on this concept:

1. What is an arithmetic sequence? How does it differ from a geometric sequence?
2. How do you determine if a sequence is quadratic or linear?
3. Can you write the general formula for the sum of the first $n$ terms of an arithmetic sequence?
4. What is the difference between finite and infinite sequences?
5. How do recurrence relations relate to sequences?

Tip: When identifying the pattern in a sequence, check for constant differences or ratios between terms to help identify if it is arithmetic or geometric.