A number series arranged in some sequence is given, One term in the series is wrong, which is given as one of the alternatives under it. Find the wrong term in that case.
1, 3, 7, 15, 31, 65, 127, 255

Options

A. 3
B. 7
C. 65
D. 31

Answer

To solve the problem of identifying the wrong term in the series 1, 3, 7, 15, 31, 65, 127, 255, we will analyze the pattern of the series step by step.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The first term is 1.
- To find the next term, we can observe that each term seems to be generated by multiplying the previous term by 2 and then adding 1.

2. **Calculate the Terms**:
- Start with the first term:
- **1st term**: 1
- **2nd term**: \(1 \times 2 + 1 = 2 + 1 = 3\)
- **3rd term**: \(3 \times 2 + 1 = 6 + 1 = 7\)
- **4th term**: \(7 \times 2 + 1 = 14 + 1 = 15\)
- **5th term**: \(15 \times 2 + 1 = 30 + 1 = 31\)
- **6th term**: \(31 \times 2 + 1 = 62 + 1 = 63\) (this is where we find a discrepancy)
- **7th term**: \(63 \times 2 + 1 = 126 + 1 = 127\)
- **8th term**: \(127 \times 2 + 1 = 254 + 1 = 255\)

3. **Identify the Wrong Term**:
- The calculated 6th term is 63, but the series has 65 listed as the 6th term. Therefore, 65 is the incorrect term.

4. **Conclusion**:
- The wrong term in the series is **65**.

### Final Answer:
The wrong term in the series is **65**.