complete the following series
7, 15, 31, 63, 127, ….

Options

A. 254
B. 265
C. 253
D. 255

Explanation

To solve the series: 7, 15, 31, 63, 127, ..., we need to identify the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- Look at the first few terms: 7, 15, 31, 63, 127.
- Notice how each term seems to be generated from the previous term.

2. **Calculate the Differences**:
- Let's calculate how each term relates to the previous one:
- From 7 to 15: \( 7 \times 2 + 1 = 15 \)
- From 15 to 31: \( 15 \times 2 + 1 = 31 \)
- From 31 to 63: \( 31 \times 2 + 1 = 63 \)
- From 63 to 127: \( 63 \times 2 + 1 = 127 \)

3. **Establish the Formula**:
- The formula we can see is:
\[ \text{Next term} = \text{Current term} \times 2 + 1 \]

4. **Apply the Formula to Find the Next Term**:
- Now, apply the formula to find the next term after 127:
\[ 127 \times 2 + 1 = 254 + 1 = 255 \]

5. **Conclusion**:
- Therefore, the next term in the series is **255**.

### Final Answer:
The completed series is: 7, 15, 31, 63, 127, **255**.

---