In the following number series only one number is wrong . Find out the wrong number.
`3" "7" "16" "32" "56" "93" "142`

Options

A. 56
B. 16
C. 32
D. 7

Answer

To find the wrong number in the series 3, 7, 16, 32, 56, 93, 142, we will analyze the differences between consecutive numbers and look for a pattern.

### Step-by-Step Solution:

1. **Write down the series**:
The given series is:
\[ 3, 7, 16, 32, 56, 93, 142 \]

2. **Calculate the differences between consecutive numbers**:
- From 3 to 7: \(7 - 3 = 4\)
- From 7 to 16: \(16 - 7 = 9\)
- From 16 to 32: \(32 - 16 = 16\)
- From 32 to 56: \(56 - 32 = 24\)
- From 56 to 93: \(93 - 56 = 37\)
- From 93 to 142: \(142 - 93 = 49\)

So, the differences are:
\[ 4, 9, 16, 24, 37, 49 \]

3. **Analyze the differences**:
Let's look at the differences again:
- \(4 = 2^2\)
- \(9 = 3^2\)
- \(16 = 4^2\)
- \(24\) (not a perfect square)
- \(37\) (not a perfect square)
- \(49 = 7^2\)

We notice that the differences seem to follow a pattern of squares for the first three differences but deviate afterwards.

4. **Identify the pattern**:
The differences appear to be:
- \(2^2 = 4\)
- \(3^2 = 9\)
- \(4^2 = 16\)
- The next difference should be \(5^2 = 25\) instead of \(24\).
- Following that, \(6^2 = 36\) should be the next difference instead of \(37\).
- Finally, \(7^2 = 49\) is correct.

5. **Correct the series**:
- Starting from \(3\):
- \(3 + 4 = 7\)
- \(7 + 9 = 16\)
- \(16 + 16 = 32\)
- **Instead of \(56\)**, we should have:
- \(32 + 25 = 57\)
- \(57 + 36 = 93\)
- \(93 + 49 = 142\)

6. **Conclusion**:
The wrong number in the series is **56**. It should be **57**.