Find the wrong number in the following number series.
17,25,38,53,79,107,140

Options

A. 79
B. 140
C. 25
D. 53

Answer

To find the wrong number in the series 17, 25, 38, 53, 79, 107, 140, we will analyze the differences between consecutive numbers and look for a pattern.

### Step-by-Step Solution:

1. **Identify the Series**:
The series given is:
\[ 17, 25, 38, 53, 79, 107, 140 \]

2. **Calculate the Differences**:
We will find the differences between each pair of consecutive numbers:
- \( 25 - 17 = 8 \)
- \( 38 - 25 = 13 \)
- \( 53 - 38 = 15 \)
- \( 79 - 53 = 26 \)
- \( 107 - 79 = 28 \)
- \( 140 - 107 = 33 \)

So, the differences are:
\[ 8, 13, 15, 26, 28, 33 \]

3. **Analyze the Differences**:
Next, we will analyze the differences to find a pattern:
- The difference between the first two differences:
- \( 13 - 8 = 5 \)
- \( 15 - 13 = 2 \)
- \( 26 - 15 = 11 \)
- \( 28 - 26 = 2 \)
- \( 33 - 28 = 5 \)

The second-level differences are:
\[ 5, 2, 11, 2, 5 \]

4. **Look for Consistency**:
The second-level differences do not show a consistent pattern. However, we notice that the difference of 11 seems out of place.

5. **Check for a Possible Correction**:
Let's assume the third term (53) is incorrect. If we replace 53 with a number that maintains a consistent pattern, we can try to find a number that fits better.

If we assume the difference after 38 should be 18 (instead of 15), we get:
\[ 38 + 18 = 56 \]

6. **Recalculate the Series**:
If we replace 53 with 56, the new series would be:
\[ 17, 25, 38, 56, 79, 107, 140 \]
Now, let's calculate the new differences:
- \( 25 - 17 = 8 \)
- \( 38 - 25 = 13 \)
- \( 56 - 38 = 18 \)
- \( 79 - 56 = 23 \)
- \( 107 - 79 = 28 \)
- \( 140 - 107 = 33 \)

The new differences are:
\[ 8, 13, 18, 23, 28, 33 \]

7. **Final Check**:
Now, the second-level differences are:
- \( 13 - 8 = 5 \)
- \( 18 - 13 = 5 \)
- \( 23 - 18 = 5 \)
- \( 28 - 23 = 5 \)
- \( 33 - 28 = 5 \)

This shows a consistent pattern of \( +5 \).

### Conclusion:
The wrong number in the series is **53**. The correct number should be **56**.