find the wrong term in givin series (27,28,37,60,111,192)

Options

A. 60
B. 28
C. 111
D. series is wrong

Answer

To find the wrong term in the series (27, 28, 37, 60, 111, 192), we will analyze the differences between consecutive terms and look for a pattern.

### Step-by-Step Solution:

1. **Identify the series**: The given series is 27, 28, 37, 60, 111, 192.

2. **Calculate the differences between consecutive terms**:
- Difference between 28 and 27: \( 28 - 27 = 1 \)
- Difference between 37 and 28: \( 37 - 28 = 9 \)
- Difference between 60 and 37: \( 60 - 37 = 23 \)
- Difference between 111 and 60: \( 111 - 60 = 51 \)
- Difference between 192 and 111: \( 192 - 111 = 81 \)

So, the differences are: 1, 9, 23, 51, 81.

3. **Analyze the differences**:
- The differences we calculated are: 1, 9, 23, 51, 81.
- Let's look for a pattern in these differences.
- The differences between these differences:
- \( 9 - 1 = 8 \)
- \( 23 - 9 = 14 \)
- \( 51 - 23 = 28 \)
- \( 81 - 51 = 30 \)

The second level differences are: 8, 14, 28, 30.

4. **Check for perfect squares**:
- The first difference (1) is \( 1^2 \).
- The second difference (9) is \( 3^2 \).
- The third difference (23) does not fit the pattern of perfect squares.
- The fourth difference (51) and fifth difference (81) are also not fitting a consistent pattern of perfect squares.

5. **Identify the wrong term**:
- If we assume that the differences should follow a pattern of perfect squares, we can check the term that disrupts this pattern.
- The difference of 23 should ideally be 25, which is \( 5^2 \).
- Therefore, to maintain the pattern, the term before 111 should have been 62 instead of 60.

6. **Conclusion**:
- The wrong term in the series is 60. It should have been 62 to maintain the pattern of differences based on perfect squares.

### Final Answer:
The wrong term in the series is **60**.