Number series (find the wrong term): 445, 221, 109, 46, 25, 11, 4 Spot the single incorrect term in the sequence and explain the governing rule.

Introduction / Context:
Some sequences are generated by a simple linear transformation applied repeatedly. Here, the pattern involves subtracting a fixed number and dividing, a common construct in reasoning tests. We will test a consistent transform between neighboring terms.

Given Data / Assumptions:

• Series: 445, 221, 109, 46, 25, 11, 4
• Exactly one term is wrong.

Concept / Approach:
Try an affine step: next = (current − k) / m for constants k and m. Testing small integers quickly reveals a fit with k = 3 and m = 2.

Step-by-Step Solution:
From 445: (445 − 3) / 2 = 442 / 2 = 221 ✔From 221: (221 − 3) / 2 = 218 / 2 = 109 ✔From 109: (109 − 3) / 2 = 106 / 2 = 53 (but the series shows 46) ✖If we correct 46 to 53, the rule continues: from 53 → (53 − 3) / 2 = 25 ✔Then 25 → (25 − 3) / 2 = 22 / 2 = 11 ✔; and 11 → (11 − 3) / 2 = 8 / 2 = 4 ✔

Verification / Alternative check:
Replacing 46 with 53 yields a perfectly consistent recurrence: next = (prev − 3) / 2 across all steps.

Why Other Options Are Wrong:

• 221, 109, 25, 11: Each follows the transformation precisely.
• 46: Breaks the single consistent rule; it should be 53.

Common Pitfalls:
It is easy to test only addition or multiplication. Always consider mixed operations like “subtract then divide,” which commonly appear in exam sequences.

Final Answer:
46