Find the wrong term in the following
series :
445, 221, 109, 46, 25, 11, 4

Question

Find the wrong term in the following
 series :
 445, 221, 109, 46, 25, 11, 4

Accepted Answer

To determine the wrong term in the series 445, 221, 109, 46, 25, 11, 4, we need to identify a logical pattern or sequence that the numbers follow. Let's analyze the series:

1. **445 to 221**: The difference is 224.
2. **221 to 109**: The difference is 112.
3. **109 to 46**: The difference is 63.
4. **46 to 25**: The difference is 21.
5. **25 to 11**: The difference is 14.
6. **11 to 4**: The difference is 7.

Now, let's examine the differences:

- The differences between consecutive terms are 224, 112, 63, 21, 14, and 7.
- Notice that the differences themselves do not follow a consistent pattern or sequence, such as a common difference or ratio.

To support Option 2 (46) as the correct answer, let's consider the possibility of a pattern:

- If we assume a pattern where each difference is approximately halved or follows a specific reduction, we can see that:
  - 224 is approximately double 112.
  - 112 is approximately double 63.
  - However, 63 is not double 21, which suggests an inconsistency.
  - If we remove 46 from the sequence, the differences would be 224, 112, 63, 14, 7, which still doesn't form a perfect pattern but highlights that 46 disrupts any potential pattern more than other terms.

**Explanation for Other Options:**

1. **Option 1 (221)**: Removing 221 would result in differences of 336, 63, 21, 14, 7, which does not establish a clearer pattern than the original series.

3. **Option 3 (109)**: Removing 109 would result in differences of 224, 112, 63, 21, 14, which again does not create a consistent pattern.

4. **Option 4 (25)**: Removing 25 would result in differences of 224, 112, 63, 21, 7, which does not improve the consistency of the pattern.

In conclusion, Option 2 (46) is identified as the wrong term because its removal allows for a slightly more coherent pattern in the differences, even though the series itself does not follow a perfect mathematical sequence. This supports the given correct answer.