29, 37, 21, 43, 13, 53, 5

Options

A. 37
B. 53
C. 13
D. 43

Explanation

To find the wrong number in the series 29, 37, 21, 43, 13, 53, 5, 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:
\[ 29, 37, 21, 43, 13, 53, 5 \]

2. **Calculate Differences:**
We will calculate the differences between consecutive numbers:
- \(37 - 29 = 8\)
- \(21 - 37 = -16\)
- \(43 - 21 = 22\)
- \(13 - 43 = -30\)
- \(53 - 13 = 40\)
- \(5 - 53 = -48\)

The differences are:
\[ 8, -16, 22, -30, 40, -48 \]

3. **Analyze the Differences:**
We observe the differences:
- The positive differences are: \(8, 22, 40\)
- The negative differences are: \(-16, -30, -48\)

4. **Identify the Pattern:**
The positive differences seem to follow a pattern:
- \(8\) (which is \(8 \times 1\))
- \(22\) (which is \(8 \times 2 + 6\))
- \(40\) (which is \(8 \times 5\))

The negative differences also seem to follow a pattern:
- \(-16\) (which is \(-8 \times 2\))
- \(-30\) (which is \(-8 \times 3 + 6\))
- \(-48\) (which is \(-8 \times 6\))

5. **Find the Missing Number:**
We notice that the expected positive difference after \(21\) should be \(24\) (which is \(8 \times 3\)), leading us to believe that the number after \(21\) should be \(21 + 24 = 45\).

6. **Replace the Wrong Number:**
Thus, we replace \(43\) with \(45\):
\[ 29, 37, 21, 45, 13, 53, 5 \]

7. **Verify the New Differences:**
Now, let's check the differences again:
- \(37 - 29 = 8\)
- \(21 - 37 = -16\)
- \(45 - 21 = 24\)
- \(13 - 45 = -32\)
- \(53 - 13 = 40\)
- \(5 - 53 = -48\)

The new differences are:
\[ 8, -16, 24, -32, 40, -48 \]

This follows the pattern of increasing and decreasing correctly.

### Conclusion:
The wrong number in the series is **43**, and it should be replaced with **45**.