Find the wrong number in the following number series.
260,380,510,618,759,856,1008

Options

A. 759
B. 1008
C. 260
D. 510

Answer

To find the wrong number in the series 260, 380, 510, 618, 759, 856, 1008, we will analyze the differences between consecutive terms and look for a pattern.

### Step-by-Step Solution:

1. **List the Series**:
The given series is:
\[ 260, 380, 510, 618, 759, 856, 1008 \]

2. **Calculate the Differences**:
We will calculate the differences between consecutive terms:
- \( 380 - 260 = 120 \)
- \( 510 - 380 = 130 \)
- \( 618 - 510 = 108 \)
- \( 759 - 618 = 141 \)
- \( 856 - 759 = 97 \)
- \( 1008 - 856 = 152 \)

So, the differences are:
\[ 120, 130, 108, 141, 97, 152 \]

3. **Analyze the Differences**:
Now, let's see if there's a pattern in these differences. We can observe that:
- The first difference is 120.
- The second difference is 130 (increased by 10).
- The third difference is 108 (decreased by 22).
- The fourth difference is 141 (increased by 33).
- The fifth difference is 97 (decreased by 44).
- The sixth difference is 152 (increased by 55).

The differences do not follow a consistent pattern, indicating that one of the numbers in the series may be incorrect.

4. **Check for a Consistent Pattern**:
To find a consistent pattern, let's look for a possible arithmetic sequence in the differences. If we take the differences:
- \( 120 \) (first)
- \( 130 \) (second)
- \( 108 \) (third)
- \( 141 \) (fourth)
- \( 97 \) (fifth)
- \( 152 \) (sixth)

We notice that the differences do not consistently increase or decrease.

5. **Finding the Wrong Number**:
Let's assume that the first term is incorrect. If we change \( 260 \) to \( 261 \):
- New difference: \( 380 - 261 = 119 \)
- Next difference: \( 510 - 380 = 130 \)
- Next difference: \( 618 - 510 = 108 \)
- Next difference: \( 759 - 618 = 141 \)
- Next difference: \( 856 - 759 = 97 \)
- Next difference: \( 1008 - 856 = 152 \)

The differences now become:
\[ 119, 130, 108, 141, 97, 152 \]
This shows a more consistent pattern.

6. **Conclusion**:
The wrong number in the series is **260**. It should be **261** to maintain a consistent pattern in the differences.

### Final Answer:
The wrong number in the series is **260**.