Here's a pattern problem designed to challenge your pattern recognition skills:

Problem:

Consider the following sequence of numbers:

2, 6, 12, 20, 30, 42, 56, ...

1. What is the next number in the sequence?
2. Determine the general formula for the $n$-th term of this sequence.

Hints:

• Look at the differences between consecutive terms.
• Once you've found a consistent pattern, try to express the relationship algebraically.

Let me know if you need help solving this or if you'd like to go into more detail!

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Here are 5 related questions to expand your learning:

1. Can you describe how the differences between the numbers change?
2. What would the 10th term of the sequence be using the formula you found?
3. Can you identify a geometric or visual pattern for this sequence?
4. What happens if you continue the pattern for 20 terms? Does the pattern remain consistent?
5. How can this pattern relate to real-world phenomena, such as physics or geometry?

Tip:

Always try to examine the differences between terms when working with number sequences. This often reveals key insights into the pattern.