Find the wrong number in the following number series?
180,200,225,254,286,322,355

Options

A. 322
B. 180
C. 286
D. 355

Answer

To find the wrong number in the series 180, 200, 225, 254, 286, 322, 355, we will analyze the differences between the consecutive terms and identify any inconsistencies.

### Step-by-Step Solution:

1. **List the Series**:
The series is: 180, 200, 225, 254, 286, 322, 355.

2. **Calculate the Differences**:
- 200 - 180 = 20
- 225 - 200 = 25
- 254 - 225 = 29
- 286 - 254 = 32
- 322 - 286 = 36
- 355 - 322 = 33

So, the differences are: 20, 25, 29, 32, 36, 33.

3. **Identify the Pattern in Differences**:
Now, let's analyze the differences:
- The first difference is 20.
- The second difference is 25 (increase of 5).
- The third difference is 29 (increase of 4).
- The fourth difference is 32 (increase of 3).
- The fifth difference is 36 (increase of 4).
- The sixth difference is 33 (decrease of 3).

We can see that the differences do not follow a consistent pattern. The expected pattern should have been a consistent decrease in the increments.

4. **Check for Consistency**:
The differences should ideally decrease by 1 each time:
- Start with 20 (no change).
- Next should be 25 (increase by 5).
- Then 29 (increase by 4).
- Next should be 32 (increase by 3).
- Then it should have been 34 (increase by 2).
- Finally, it should have been 36 (increase by 1).

5. **Identify the Wrong Number**:
The difference of 36 is inconsistent with the expected pattern. If we follow the pattern, the correct number after 286 should have been 320 (286 + 34).

Therefore, the number 322 is incorrect.

6. **Conclusion**:
The wrong number in the series is **322**.