The sequence \( 6, 8, 18, 48, 116, \,? \) appears to follow a pattern where each term is generated based on the previous ones. Let's analyze the differences between consecutive terms:

1. \( 8 - 6 = 2 \)
2. \( 18 - 8 = 10 \)
3. \( 48 - 18 = 30 \)
4. \( 116 - 48 = 68 \)

Now, observe the differences between the differences:

1. \( 10 - 2 = 8 \)
2. \( 30 - 10 = 20 \)
3. \( 68 - 30 = 38 \)

These second differences aren't consistent, but let's look at the third differences:

1. \( 20 - 8 = 12 \)
2. \( 38 - 20 = 18 \)

The third differences show a pattern, suggesting that the next third difference might be \( 18 + 6 = 24 \). If we apply this backward:

1. The next second difference would be \( 38 + 24 = 62 \).
2. The next first difference would be \( 68 + 62 = 130 \).

So, the next term in the sequence would be:

\[ 116 + 130 = 246 \]

Thus, the next term in the sequence is **246**.

Would you like more details, or do you have any questions? Here are five related questions you might find interesting:

1. What is the significance of identifying patterns in sequences?
2. How can we determine the general formula for a sequence?
3. How do arithmetic and geometric sequences differ?
4. Can you identify the pattern in a different sequence of your choice?
5. What are some real-life applications of recognizing numerical patterns?

**Tip:** When analyzing a sequence, consider looking at the differences between terms, and if necessary, the differences of those differences, to uncover hidden patterns.

Explore the pattern in the sequence 6, 8, 18, 48, 116, ? and discover the next term. This problem involves analyzing differences between consecutive terms and identifying hidden patterns. Suitable for advanced high school students and anyone interested in sequence analysis.

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