In each of the following number series , a wrong number is given ,find out the wrong number -----
50 51 47 56 42 65 29

Options

A. 51
B. 47
C. 56
D. 42

Answer

To find the wrong number in the series 50, 51, 47, 56, 42, 65, 29, we will analyze the pattern in the series step by step.

1. **Identify the Pattern**:
- The series appears to alternate between adding and subtracting squares of integers.
- Let's denote the terms as follows:
- \( a_1 = 50 \)
- \( a_2 = 51 \)
- \( a_3 = 47 \)
- \( a_4 = 56 \)
- \( a_5 = 42 \)
- \( a_6 = 65 \)
- \( a_7 = 29 \)

2. **Calculate Each Term**:
- Start with the first term \( a_1 = 50 \).
- **Second term**: \( a_2 = a_1 + 1^2 = 50 + 1 = 51 \) (Correct)
- **Third term**: \( a_3 = a_2 - 2^2 = 51 - 4 = 47 \) (Correct)
- **Fourth term**: \( a_4 = a_3 + 3^2 = 47 + 9 = 56 \) (Correct)
- **Fifth term**: \( a_5 = a_4 - 4^2 = 56 - 16 = 40 \) (Expected)
- **Sixth term**: \( a_6 = a_5 + 5^2 = 40 + 25 = 65 \) (Correct)
- **Seventh term**: \( a_7 = a_6 - 6^2 = 65 - 36 = 29 \) (Correct)

3. **Identify the Wrong Number**:
- In the calculation for the fifth term, we expected \( a_5 \) to be 40, but it is given as 42 in the series.
- Therefore, the wrong number in the series is **42**.

4. **Conclusion**:
- The wrong number in the series is **42**. The correct number should be **40**.