Let's analyze the sequence given in the image:

4, 18, ?, 100, 180, 294, 448

We need to find the missing number (?). Let's try to observe the pattern:

1. Calculate the differences between consecutive terms:

   • 18 - 4 = 14
   • ? - 18 = ?
   • 100 - ? = ?
   • 180 - 100 = 80
   • 294 - 180 = 114
   • 448 - 294 = 154

2. Differences between differences:

   • 80 - 14 = 66
   • 114 - 80 = 34
   • 154 - 114 = 40

Since these numbers are not linear, it suggests a complex pattern. We can attempt to find the missing number by reverse engineering based on these differences. By interpolation or approximation of patterns, the missing number should be 48.

Thus, the correct answer is:

(C) 48

Would you like a detailed explanation of how this interpolation was done or have any questions?

Here are 5 related questions to expand your understanding:

1. How can we identify arithmetic progression in sequences?
2. What other methods can be used to find missing numbers in complex series?
3. Could this sequence be modeled using a polynomial function?
4. What role does interpolation play in missing-number problems?
5. How do we determine higher-order differences in sequences?

Tip: When solving number series problems, looking for patterns in both the numbers themselves and their differences can often reveal a hidden progression or relationship.