3,7,15,39,63,127,255,511

Options

A. 7
B. 15
C. 39
D. 63

Answer

To solve the problem of identifying the wrong term in the series 3, 7, 15, 39, 63, 127, 255, 511, we will analyze the pattern in the series step by step.

### Step-by-Step Solution:

1. **Identify the Pattern**:
We will look for a consistent pattern in the series. The first few terms are:
- 3
- 7
- 15
- 39
- 63
- 127
- 255
- 511

2. **Check Multiplication and Addition**:
Let's check if each term can be derived from the previous term using a multiplication by 2 and then adding 1.
- From 3 to 7:
\[ 3 \times 2 + 1 = 6 + 1 = 7 \]
- From 7 to 15:
\[ 7 \times 2 + 1 = 14 + 1 = 15 \]
- From 15 to 39:
\[ 15 \times 2 + 1 = 30 + 1 = 31 \quad (\text{This should be } 39) \]
- From 39 to 63:
\[ 39 \times 2 + 1 = 78 + 1 = 79 \quad (\text{This should be } 63) \]
- From 63 to 127:
\[ 63 \times 2 + 1 = 126 + 1 = 127 \]
- From 127 to 255:
\[ 127 \times 2 + 1 = 254 + 1 = 255 \]
- From 255 to 511:
\[ 255 \times 2 + 1 = 510 + 1 = 511 \]

3. **Identify the Wrong Term**:
From the calculations, we see that:
- The transition from 15 to 39 does not follow the pattern since it should have been 31.
- The transition from 39 to 63 also does not follow the pattern since it should have been 79.
Therefore, the term **39** is identified as the wrong term in the series.

4. **Conclusion**:
The wrong term in the series is **39**.