400, 396, 392, 380, 360, 330, 288

Options

A. 1. 380
B. 2. 396
C. 3. 400
D. 4. 288

Explanation

To solve the problem, we need to analyze the given series: 400, 396, 392, 380, 360, 330, 288. We will look for a pattern in the differences between the consecutive numbers.

### Step-by-Step Solution:

1. **List the Series**:
The series is:
\[ 400, 396, 392, 380, 360, 330, 288 \]

2. **Calculate the Differences**:
We will find the differences between each pair of consecutive numbers:
- \(400 - 396 = 4\)
- \(396 - 392 = 4\)
- \(392 - 380 = 12\)
- \(380 - 360 = 20\)
- \(360 - 330 = 30\)
- \(330 - 288 = 42\)

So, the differences are:
\[ 4, 4, 12, 20, 30, 42 \]

3. **Calculate the Second Differences**:
Now, we will find the differences of the differences:
- \(4 - 4 = 0\)
- \(12 - 4 = 8\)
- \(20 - 12 = 8\)
- \(30 - 20 = 10\)
- \(42 - 30 = 12\)

The second differences are:
\[ 0, 8, 8, 10, 12 \]

4. **Identify the Pattern**:
The first two differences are the same (0 and 8), but then the differences increase. The expected pattern seems to suggest that the differences should be consistent.

5. **Check for Consistency**:
If we assume the second difference should be consistent, we can see that the jump between the differences is not uniform. The second difference should ideally follow a predictable pattern.

6. **Find the Wrong Number**:
If we assume that the second difference should be consistent, we notice that the difference of 12 (from 392 to 380) is larger than expected. If we change 396 to 398, we can check:
- The new series would be:
\[ 400, 398, 392, 380, 360, 330, 288 \]
- The new differences would be:
\[ 2, 6, 12, 20, 30, 42 \]
- The second differences would then be:
\[ 4, 6, 8, 10, 12 \]
This shows a consistent increase.

7. **Conclusion**:
The wrong number in the series is **396**, and it should be **398** to maintain a consistent pattern.