A number series is given with one term missing. Choose the correct alternative from the given options that will complete the series. ?, 9, 19, 39, 79

Introduction / Context:
In this number series, the missing term appears at the beginning. The pattern is based on differences that grow by a constant factor. The learner must work backward using the same rule that governs the forward movement of the series. This builds skill in both forward and backward reasoning with numerical patterns.

Given Data / Assumptions:
- Series: ?, 9, 19, 39, 79. - The first term is missing. - Differences between known terms suggest a pattern.

Concept / Approach:
The approach is to compute the differences between consecutive known terms and observe how those differences change. If the differences follow a consistent rule such as doubling, that rule can be applied backward to determine the initial term. Because the first term is missing, analysis begins from the second term onward.

Step-by-Step Solution:
Step 1: Find differences between known terms. 9 to 19: difference = 10. 19 to 39: difference = 20. 39 to 79: difference = 40. Step 2: The differences are 10, 20, and 40, which clearly double each time. Step 3: If the pattern extends backward, then the difference between the missing first term and 9 should be 5, half of 10. Step 4: Therefore, 9 minus 5 must equal the missing first term. Step 5: Calculate 9 - 5 = 4.

Verification / Alternative check:
Rebuild the full series using the discovered rule: start with 4, add 5 to get 9, then add 10 to get 19, add 20 to get 39, and finally add 40 to get 79. This generates 4, 9, 19, 39, 79, which matches the pattern perfectly and confirms that 4 is the correct starting term.

Why Other Options Are Wrong:
- Option 9 would make the first two terms equal and break the doubling differences pattern. - Option 7 would give a difference of 2 between the first two terms, which does not fit with the later differences of 10, 20, and 40. - Option 6 would lead to a difference of 3 between the first two terms, again inconsistent with the doubling pattern.

Common Pitfalls:
Learners may try to apply a direct formula to the terms instead of first examining the differences. Another error is to assume arbitrary starting values without checking consistency across all steps. Always verify that the same rule explains every transition in the series, both forward and backward.

Final Answer:
The missing first term is 4, so the correct option is 4.