6.5 11.8 22.4 38.3 59.5 87.3 117.8

Options

A. 22.4
B. 59.5
C. 11.8
D. 87.3

Explanation

To find the wrong number in the series 6.5, 11.8, 22.4, 38.3, 59.5, 87.3, 117.8, we will analyze the differences between consecutive terms and identify the pattern.

### Step-by-Step Solution:

1. **Identify the Series**:
The series given is:
- 6.5, 11.8, 22.4, 38.3, 59.5, 87.3, 117.8

2. **Calculate the Differences**:
We will calculate the differences between each pair of consecutive numbers:
- Difference between 11.8 and 6.5:
\[ 11.8 - 6.5 = 5.3 \]
- Difference between 22.4 and 11.8:
\[ 22.4 - 11.8 = 10.6 \]
- Difference between 38.3 and 22.4:
\[ 38.3 - 22.4 = 15.9 \]
- Difference between 59.5 and 38.3:
\[ 59.5 - 38.3 = 21.2 \]
- Difference between 87.3 and 59.5:
\[ 87.3 - 59.5 = 27.8 \]
- Difference between 117.8 and 87.3:
\[ 117.8 - 87.3 = 30.5 \]

The differences are:
- 5.3, 10.6, 15.9, 21.2, 27.8, 30.5

3. **Analyze the Differences**:
Now we will analyze the pattern in the differences:
- The first difference is 5.3.
- The second difference is approximately double the first: \(5.3 \times 2 = 10.6\).
- The third difference is approximately \(5.3 \times 3 = 15.9\).
- The fourth difference should be \(5.3 \times 4 = 21.2\).
- The fifth difference should be \(5.3 \times 5 = 26.5\).
- The sixth difference should be \(5.3 \times 6 = 31.8\).

4. **Identify the Anomaly**:
By comparing the calculated differences with the actual differences:
- The fourth difference is 21.2 (which is correct).
- The fifth difference is 27.8 (but it should be 26.5).
- The sixth difference is 30.5 (which is correct).

This indicates that the number 87.3 is incorrect because it leads to an incorrect difference.

5. **Calculate the Correct Number**:
To find the correct number, we replace 87.3 with the expected value:
\[ 59.5 + 26.5 = 86 \]

6. **Conclusion**:
The wrong number in the series is **87.3**, and it should be **86**.