The missing number of the sequence 0, 2, 8, 18,_, 50 is :

Options

A. 28
B. 30
C. 32
D. 36

Answer

To find the missing number in the sequence 0, 2, 8, 18, _, 50, we can analyze the pattern in the numbers provided.

### Step 1: Identify the pattern
Let's look at the numbers in the sequence:
- 0
- 2
- 8
- 18
- ?
- 50

### Step 2: Find a formula
We can observe that each number seems to follow a specific formula. Let's express each number in terms of its position in the sequence:
- The 1st number (0) can be expressed as \(2 \times 0^2 = 0\)
- The 2nd number (2) can be expressed as \(2 \times 1^2 = 2\)
- The 3rd number (8) can be expressed as \(2 \times 2^2 = 8\)
- The 4th number (18) can be expressed as \(2 \times 3^2 = 18\)

### Step 3: Calculate the missing number
Following the same pattern, the 5th number can be expressed as:
- The 5th number (missing) is \(2 \times 4^2 = 2 \times 16 = 32\)

### Step 4: Confirm the next number
To confirm, we can calculate the 6th number:
- The 6th number (50) can be expressed as \(2 \times 5^2 = 2 \times 25 = 50\)

### Conclusion
Thus, the missing number in the sequence is **32**.