In the following question, a number series is given with one term missing. Select the missing number from the given series that correctly continues the pattern: 6, 9, 15, 24, 39, 63, ?

Introduction / Context:
This is a classic example of a Fibonacci style number series, where each term after the first two is obtained by combining the previous two terms. Recognising such patterns is important in verbal reasoning and quantitative aptitude exams. The series given is 6, 9, 15, 24, 39, 63, ?, and we must find the missing term at the end.

Given Data / Assumptions:

• Series: 6, 9, 15, 24, 39, 63, ?
• Options: 97, 102, 115, 127.
• We assume a single consistent rule drives the progression of terms.

Concept / Approach:
For series where each term looks roughly like the sum of the previous two, a Fibonacci type pattern is suspected. Instead of focusing on fixed differences, we check whether from some point onward each term equals the sum of the previous two terms. If this holds from the third term onward, we can safely extend it to find the next term.

Step-by-Step Solution:
Step 1: Test the relation T(n) = T(n-1) + T(n-2).Check 15: 6 + 9 = 15. This matches.Check 24: 9 + 15 = 24. This matches.Check 39: 15 + 24 = 39. This matches.Check 63: 24 + 39 = 63. This also matches.Step 2: Use the same rule for the missing term.Next term = 39 + 63 = 102.

Verification / Alternative check:
Write the complete series including the found term: 6, 9, 15, 24, 39, 63, 102. From the third term onward each term is exactly the sum of the two preceding terms. This is precisely how a Fibonacci type sequence behaves, and no term violates the rule. Therefore, 102 fits perfectly and ensures the structure of the series remains intact.

Why Other Options Are Wrong:
97: 39 + 63 is not 97, so it cannot be the next term in a Fibonacci style pattern.115: Also does not equal 39 + 63, hence inconsistent with the established rule.127: Again does not match the required sum of 102.

Common Pitfalls:
Some students incorrectly focus on differences between consecutive terms: 3, 6, 9, 15, 24 and then attempt to find a second level pattern in those differences. While a pattern exists there too, it is more complicated than simply noticing that the main series is formed by summing the previous two terms. Always check for Fibonacci type patterns early when the numbers grow in this manner.

Final Answer:
The missing term that continues the Fibonacci style sequence is 102.