Number Series Analysis

The question asks us to identify the missing number in the following numerical series:

73, 97, 115, ?, 157, 181, 199

To find the missing term, we need to analyze the pattern or the relationship between the consecutive numbers in the series.

Step-by-Step Pattern Identification

Let's calculate the difference between each pair of consecutive numbers:

• Difference between the 2nd and 1st term: $97 - 73 = 24$
• Difference between the 3rd and 2nd term: $115 - 97 = 18$
• Difference between the 6th and 5th term: $181 - 157 = 24$
• Difference between the 7th and 6th term: $199 - 181 = 18$

Observing these differences, we can see a repeating pattern of differences:

The pattern of differences appears to be alternating between $24$ and $18$.

Calculating the Missing Term

Following the identified alternating pattern (24, 18, 24, 18, ...):

1. The difference between the 3rd term (115) and the 4th term (?) should be $24$.
2. Calculation: $115 + 24 = 139$.
3. Let's verify this with the next step. The difference between the 4th term (139) and the 5th term (157) should be $18$.
4. Verification: $139 + 18 = 157$. This matches the series.

Therefore, the missing number in the series is 139.

Conclusion

The series follows a pattern where the difference between consecutive terms alternates between $24$ and $18$. Based on this pattern, the number that should replace the question mark (?) is $139$.