What should come in place of question mark(?) in the following number series ?
7 5 7 17 63 ?

Options

A. 321
B. 309
C. 305
D. 301

Answer

To find the missing number in the series 7, 5, 7, 17, 63, ?, we will analyze the pattern step by step.

### Step 1: Identify the pattern
Let's look at the transitions between the numbers in the series:

1. From 7 to 5
2. From 5 to 7
3. From 7 to 17
4. From 17 to 63

### Step 2: Analyze the first transition (7 to 5)
To go from 7 to 5:
- We can see that \(7 \times 1 - 2 = 5\)

### Step 3: Analyze the second transition (5 to 7)
To go from 5 to 7:
- We can see that \(5 \times 2 - 3 = 7\)

### Step 4: Analyze the third transition (7 to 17)
To go from 7 to 17:
- We can see that \(7 \times 3 - 4 = 17\)

### Step 5: Analyze the fourth transition (17 to 63)
To go from 17 to 63:
- We can see that \(17 \times 4 - 5 = 63\)

### Step 6: Identify the next transition (63 to ?)
Following the established pattern:
- The next operation should involve multiplying by 5 and subtracting 6.

### Step 7: Calculate the missing number
Now we calculate:
- \(63 \times 5 - 6\)
- First, calculate \(63 \times 5 = 315\)
- Then, subtract 6: \(315 - 6 = 309\)

### Conclusion
Thus, the number that should come in place of the question mark is **309**.