Consider the following increasing number series: 8, 15, 28, 53, ?, 199. Determine which number should replace the question mark to continue the pattern correctly.

Introduction / Context:
This is a classic number series with one missing term. The pattern is not a simple arithmetic progression, so we must pay attention to how the differences between consecutive terms themselves change. Such patterns often involve doubling, halving or adding fixed numbers to the previous difference.

Given Data / Assumptions:

• Series: 8, 15, 28, 53, ?, 199.
• Exactly one term is missing.
• The pattern is expected to be systematic and based on simple arithmetic operations.

Concept / Approach:
We first compute the differences between consecutive terms. If those differences follow a recognisable pattern, we can predict the next differences and hence the missing term. In many exam series, the differences follow a rule like d_n+1 = 2 * d_n - 1 or similar relations.

Step-by-Step Solution:
1. Begin with the given terms: 8, 15, 28, 53, ?, 199. 2. Compute known differences: 15 - 8 = 7 28 - 15 = 13 53 - 28 = 25 3. The first three differences are 7, 13, 25. Notice that these differences themselves are increasing quite rapidly. 4. Observe the relationship: 13 = 2 * 7 - 1 and 25 = 2 * 13 - 1. So each new difference equals double the previous difference minus 1. 5. Apply the same rule to find the next difference: Next difference = 2 * 25 - 1 = 50 - 1 = 49. 6. Add this to the last known term 53 to get the missing term: Missing term = 53 + 49 = 102. 7. Now compute the final difference to reach 199: 199 - 102 = 97. 8. Check the rule again: 97 should equal 2 * 49 - 1, which is indeed 98 - 1 = 97.

Verification / Alternative check:
List all terms with the inferred differences: 8 8 + 7 = 15 15 + 13 = 28 28 + 25 = 53 53 + 49 = 102 102 + 97 = 199 Check the difference pattern again: 7, 13, 25, 49, 97 where each term is 2 * previous - 1. The series is perfectly consistent.

Why Other Options Are Wrong:

• 101, 103, 104: Any of these values would produce final differences that break the rule d_n+1 = 2 * d_n - 1. None of them lead to 199 with the correct next difference of 97, so they are inconsistent with the discovered pattern.

Common Pitfalls:
A typical mistake is to assume that the differences must increase by a fixed amount (for example +6 or +8) and stop the analysis too early. Since 7, 13, 25 do not show a simple constant increment, some candidates guess randomly. The correct strategy is to test multiplicative patterns in the differences, such as doubling and then adding or subtracting a small constant, until a consistent rule emerges for all terms.

Final Answer:
The number that correctly completes the series is 102.