1, 3, 7, 15, 27, 63, 127

Options

A. 7
B. 15
C. 27
D. 63

Explanation

To solve the problem, we need to identify the pattern in the given series: 1, 3, 7, 15, 27, 63, 127.

### Step-by-Step Solution:

1. **Identify the Pattern**:
Let's analyze the series step by step.
- Start with the first number: **1**.
- The next number is **3**.
- The difference between them is: 3 - 1 = **2**.

2. **Continue the Pattern**:
- The next number is **7**.
- The difference from the previous number (3) is: 7 - 3 = **4**.

3. **Next Differences**:
- The next number is **15**.
- The difference from the previous number (7) is: 15 - 7 = **8**.

4. **Next Number**:
- The next number is **27**.
- The difference from the previous number (15) is: 27 - 15 = **12**.

5. **Next Number**:
- The next number is **63**.
- The difference from the previous number (27) is: 63 - 27 = **36**.

6. **Final Number**:
- The last number is **127**.
- The difference from the previous number (63) is: 127 - 63 = **64**.

7. **Identify the Pattern in Differences**:
- The differences we calculated are: 2, 4, 8, 12, 36, 64.
- Notice that the differences themselves are not following a consistent pattern. However, we can observe that the differences seem to be doubling at certain points.

8. **Finding the Error**:
- If we look closely, the difference from 15 to 27 (which is 12) seems to be inconsistent with the doubling pattern observed in the other differences.
- The correct next number after 15 should be 31 (15 + 16, where 16 is the next power of 2 after 8).
- Therefore, the number **27** is incorrect; it should be **31**.

### Conclusion:
The wrong number in the series is **27**.