17, 18, 22, 31, 46, 72

Options

A. 17
B. 18
C. 31
D. 46

Explanation

To solve the problem of identifying the wrong number in the series 17, 18, 22, 31, 46, 72, we will analyze the differences between consecutive terms and look for a pattern.

### Step-by-Step Solution:

1. **Identify the Series**: The given series is 17, 18, 22, 31, 46, 72.

2. **Calculate the Differences**:
- 18 - 17 = 1
- 22 - 18 = 4
- 31 - 22 = 9
- 46 - 31 = 15
- 72 - 46 = 26

So, the differences between consecutive terms are: 1, 4, 9, 15, 26.

3. **Analyze the Differences**:
- The differences themselves seem to follow a pattern. Let's look at the differences of the differences:
- 4 - 1 = 3
- 9 - 4 = 5
- 15 - 9 = 6
- 26 - 15 = 11

The second differences are: 3, 5, 6, 11.

4. **Look for a Pattern**:
- The first differences (1, 4, 9, 15, 26) can be analyzed further:
- The differences of these differences are not consistent, suggesting that there might be an error in the series.

5. **Check the Last Two Terms**:
- If we assume the last term should follow a certain pattern, we can check if 46 is the correct number.
- If we take the difference from 31 to 46, we see that it is 15. If we assume the next number should be 47 instead of 46, we can check:
- 31 + 16 = 47 (which is consistent with the increasing pattern).

6. **Conclusion**:
- Since replacing 46 with 47 fits the pattern of differences better, we conclude that 46 is the wrong number in the series.

### Final Answer:
The wrong number in the series is **46**.

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