15,31, 63,127,255 (…)

Options

A. 513
B. 511
C. 517
D. 523

Answer

To find the next term in the series 15, 31, 63, 127, 255, we can observe the pattern in the series. Let's break it down step by step.

### Step 1: Identify the pattern in the series
The given series is:
- 15
- 31
- 63
- 127
- 255

### Step 2: Analyze the relationship between consecutive terms
Let's look at the relationship between each term:
- From 15 to 31:
- \( 15 \times 2 + 1 = 31 \)
- From 31 to 63:
- \( 31 \times 2 + 1 = 63 \)
- From 63 to 127:
- \( 63 \times 2 + 1 = 127 \)
- From 127 to 255:
- \( 127 \times 2 + 1 = 255 \)

### Step 3: Formulate the rule
We can see that each term can be derived from the previous term using the formula:
\[ \text{Next term} = \text{Current term} \times 2 + 1 \]

### Step 4: Apply the rule to find the next term
Now, let's apply this rule to find the next term after 255:
- \( 255 \times 2 + 1 = 510 + 1 = 511 \)

### Conclusion
Thus, the next term in the series is **511**.