What will come in place of question mark (? ) in the following number series ?
7 `" " 48 " " 286 " " 1427 " " ? " " 17107`

Options

A. 5504
B. 5604
C. 5704
D. 5804

Answer

To find the missing number in the series: 7, ?, 48, ?, 286, ?, 1427, ?, ?, 17107, we need to identify the pattern in the series.

### Step 1: Identify the relationship between the numbers
Let's analyze the relationship between the numbers given in the series:

1. **From 7 to 48**:
- We can see that \(7 \times 7 - 1 = 49 - 1 = 48\).

2. **From 48 to 286**:
- Here, we can observe that \(48 \times 6 = 288\) and then \(288 - 2 = 286\).

3. **From 286 to 1427**:
- For this transition, we can see that \(286 \times 5 - 3 = 1430 - 3 = 1427\).

### Step 2: Continuing the pattern
Now, we can see a pattern where the multiplier decreases by 1 each time, and the number subtracted increases by 1 each time.

- The pattern for the multipliers is: 7, 6, 5, and the next should be 4.
- The pattern for the subtracted numbers is: 1, 2, 3, and the next should be 4.

### Step 3: Calculate the missing number
Now we can find the missing number after 1427:

- **From 1427 to ?**:
- We will multiply 1427 by 4 and subtract 4.
- Calculation: \(1427 \times 4 - 4 = 5708 - 4 = 5704\).

### Step 4: Verify the next number
To ensure our answer is correct, we can also check the next number in the series:

- **From ? to 17107**:
- We will multiply 5704 by 3 and subtract 5.
- Calculation: \(5704 \times 3 - 5 = 17112 - 5 = 17107\).

Thus, the missing number in the series is **5704**.

### Final Answer
The number that comes in place of the question mark (?) is **5704**.

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