Odd Man Out – Identify the inconsistent term in the pattern: Sequence: 4, 9, 19, 39, 79, 160, 319

Introduction / Context:
This is an odd-man-out question on number series. The goal is to detect the intended rule driving the sequence and then spot the single term that violates that rule. Such patterns frequently involve simple recurrences like multiply-and-add or consistent differences.

Given Data / Assumptions:

• Sequence shown: 4, 9, 19, 39, 79, 160, 319
• Assume a uniform rule is intended for all steps.

Concept / Approach:
A common pattern is “double the previous number, then add 1.” We test each transition for the rule a(n+1) = 2*a(n) + 1 and see where the sequence breaks.

Step-by-Step Solution:
From 4: 2*4 + 1 = 9 ✔From 9: 2*9 + 1 = 19 ✔From 19: 2*19 + 1 = 39 ✔From 39: 2*39 + 1 = 79 ✔From 79: expected 2*79 + 1 = 159; given term is 160 ✖From 159 (if correct): 2*159 + 1 = 319, which matches the last term ✔

Verification / Alternative check:
If we replace 160 with 159, the entire chain satisfies the single rule without exception. The last term 319 confirms the rule by equaling 2*159 + 1.

Why Other Options Are Wrong:
39, 79, and 319 each comply with “double + 1.” Only 160 breaks the recurrence; 159 would have fit.

Common Pitfalls:
Looking for changing offsets (like +1, +1, +2) instead of noticing a consistent recurrence; or assuming a late-series deviation implies multiple rules.

Final Answer:
160