in the following number series only one is wrong . Find out the wrong number .
`7" "18 " "40" "106" "183" "282 " "403`

Options

A. 18
B. 282
C. 40
D. 106

Answer

To find the wrong number in the series `7, 18, 40, 106, 183, 282, 403`, we will analyze the differences between consecutive numbers and look for a pattern.

### Step-by-Step Solution:

1. **Identify the series**: The given series is:
\[ 7, 18, 40, 106, 183, 282, 403 \]

2. **Calculate the differences between consecutive numbers**:
- From 7 to 18:
\[ 18 - 7 = 11 \]
- From 18 to 40:
\[ 40 - 18 = 22 \]
- From 40 to 106:
\[ 106 - 40 = 66 \]
- From 106 to 183:
\[ 183 - 106 = 77 \]
- From 183 to 282:
\[ 282 - 183 = 99 \]
- From 282 to 403:
\[ 403 - 282 = 121 \]

So the differences are:
\[ 11, 22, 66, 77, 99, 121 \]

3. **Analyze the differences**:
- The differences do not follow a clear pattern initially, so we will look for a second level of differences.
- Calculate the differences of the differences:
- From 11 to 22:
\[ 22 - 11 = 11 \]
- From 22 to 66:
\[ 66 - 22 = 44 \]
- From 66 to 77:
\[ 77 - 66 = 11 \]
- From 77 to 99:
\[ 99 - 77 = 22 \]
- From 99 to 121:
\[ 121 - 99 = 22 \]

The second level differences are:
\[ 11, 44, 11, 22, 22 \]

4. **Look for a consistent pattern**:
- The first difference of 11 appears twice, and we see a jump to 44, which seems inconsistent.
- If we consider that the differences should be increasing in a consistent manner, we can hypothesize that there might be an error in the number 40.

5. **Propose a correction**:
- If we replace 40 with a number that fits the pattern, we can try adding 33 to 18:
\[ 18 + 33 = 51 \]
- Now, let's check the next differences:
- From 7 to 18: 11
- From 18 to 51:
\[ 51 - 18 = 33 \]
- From 51 to 106:
\[ 106 - 51 = 55 \]
- From 106 to 183:
\[ 183 - 106 = 77 \]
- From 183 to 282:
\[ 282 - 183 = 99 \]
- From 282 to 403:
\[ 403 - 282 = 121 \]

6. **Conclusion**:
- The corrected series is:
\[ 7, 18, 51, 106, 183, 282, 403 \]
- Therefore, the wrong number in the original series is **40**, which should be replaced by **51**.