1 2 8 21 88 445

Options

A. 24.5
B. 25
C. 25.5
D. None of these

Explanation

To solve the problem of identifying the wrong number in the series: 1, 2, 8, 21, 88, 445, we will analyze the pattern step by step.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is 1, 2, 8, 21, 88, 445.

2. **Look for Patterns**: We need to find a consistent pattern that connects these numbers. Let's examine the transitions between each number.

3. **From 1 to 2**:
- We can see that \(1 \times 1 + 1 = 2\).
- So, the first operation can be described as: \(1 \times 1 + 1 = 2\).

4. **From 2 to 8**:
- Here, we can try \(2 \times 2 + 2\).
- This gives us \(2 \times 2 = 4\) and \(4 + 2 = 6\), which is not equal to 8.
- Let's try another approach: \(2 \times 3 + 2 = 8\) does work.
- So, this operation can be described as: \(2 \times 3 + 2 = 8\).

5. **From 8 to 21**:
- For this transition, let's check \(8 \times 2 + 5\).
- This gives us \(8 \times 2 = 16\) and \(16 + 5 = 21\).
- So, this operation can be described as: \(8 \times 2 + 5 = 21\).

6. **From 21 to 88**:
- Now, we check \(21 \times 4 + 4\).
- This gives us \(21 \times 4 = 84\) and \(84 + 4 = 88\).
- So, this operation can be described as: \(21 \times 4 + 4 = 88\).

7. **From 88 to 445**:
- Next, we check \(88 \times 5 + 5\).
- This gives us \(88 \times 5 = 440\) and \(440 + 5 = 445\).
- So, this operation can be described as: \(88 \times 5 + 5 = 445\).

8. **Identifying the Wrong Number**:
- Now, let's summarize the operations:
- \(1 \times 1 + 1 = 2\)
- \(2 \times 3 + 2 = 8\) (this seems inconsistent)
- \(8 \times 2 + 5 = 21\)
- \(21 \times 4 + 4 = 88\)
- \(88 \times 5 + 5 = 445\)
- The operation from 2 to 8 does not follow the previously established pattern. It should have been \(2 \times 2 + 2 = 6\) instead of 8.

9. **Conclusion**:
- The wrong number in the series is **8**. The correct number should be **6**.