Find the wrong number in the following number series.
-1,1,2,6,14,30,62

Options

A. 1
B. 62
C. -1
D. 14

Answer

To find the wrong number in the series -1, 1, 2, 6, 14, 30, 62, we will analyze the differences between the consecutive terms and look for a pattern.

### Step-by-Step Solution:

1. **Write down the series**:
The series given is: -1, 1, 2, 6, 14, 30, 62.

2. **Calculate the differences between consecutive terms**:
- From -1 to 1: \(1 - (-1) = 2\)
- From 1 to 2: \(2 - 1 = 1\)
- From 2 to 6: \(6 - 2 = 4\)
- From 6 to 14: \(14 - 6 = 8\)
- From 14 to 30: \(30 - 14 = 16\)
- From 30 to 62: \(62 - 30 = 32\)

So, the differences are: 2, 1, 4, 8, 16, 32.

3. **Analyze the pattern in the differences**:
The differences seem to follow a pattern of doubling after the first two terms:
- 2 (1st difference)
- 1 (2nd difference)
- 4 (2 * 2)
- 8 (2 * 4)
- 16 (2 * 8)
- 32 (2 * 16)

4. **Identify the inconsistency**:
The second difference (1) does not fit the doubling pattern. If we assume the second term should follow the pattern, it should have been 0 instead of 1.

5. **Replace the incorrect term**:
If we replace 1 with 0, the series would be:
-1, 0, 2, 6, 14, 30, 62.

6. **Recalculate the differences with the corrected term**:
- From -1 to 0: \(0 - (-1) = 1\)
- From 0 to 2: \(2 - 0 = 2\)
- From 2 to 6: \(6 - 2 = 4\)
- From 6 to 14: \(14 - 6 = 8\)
- From 14 to 30: \(30 - 14 = 16\)
- From 30 to 62: \(62 - 30 = 32\)

The new differences are: 1, 2, 4, 8, 16, 32, which now follows the doubling pattern.

7. **Conclusion**:
The wrong number in the series is **1**. The correct series should be -1, 0, 2, 6, 14, 30, 62.