7, 15, 33, 69, 149, 307

Options

A. 15
B. 33
C. 69
D. 307

Explanation

To solve the given series: 7, 15, 33, 69, 149, 307, we need to identify the pattern in the series and determine which number is incorrect.

### Step-by-Step Solution:

1. **Identify the first number**: The first number in the series is 7.

2. **Find the next number**:
- To get from 7 to the next number (15), we can double 7 and add 1.
- Calculation: \( 7 \times 2 + 1 = 14 + 1 = 15 \)

3. **Continue the pattern**:
- Now, let's find the next number after 15 (which is 33).
- We double 15 and add 3.
- Calculation: \( 15 \times 2 + 3 = 30 + 3 = 33 \)

4. **Next number after 33**:
- We double 33 and add 5.
- Calculation: \( 33 \times 2 + 5 = 66 + 5 = 71 \)

5. **Next number after 71**:
- We double 71 and add 7.
- Calculation: \( 71 \times 2 + 7 = 142 + 7 = 149 \)

6. **Next number after 149**:
- We double 149 and add 9.
- Calculation: \( 149 \times 2 + 9 = 298 + 9 = 307 \)

7. **Check the series**:
- The series we derived is: 7, 15, 33, 71, 149, 307.
- The number 69 in the original series is incorrect. It should be 71.

### Conclusion:
The incorrect number in the series is **69**, and it should be replaced with **71**.