11, 23, 48, 99, …., 409.

Options

A. 200
B. 202
C. 201
D. 205

Explanation

To solve the series 11, 23, 48, 99, …, 409, we will analyze the pattern in the series step by step.

### Step 1: Identify the pattern
We start with the first term, which is 11. Let's see how the subsequent terms are derived from it.

### Step 2: Calculate the second term
- The first term is 11.
- If we multiply 11 by 2, we get 22.
- Adding 1 to 22 gives us the second term:
\[ 11 \times 2 + 1 = 22 + 1 = 23 \]

### Step 3: Calculate the third term
- The second term is 23.
- If we multiply 23 by 2, we get 46.
- Adding 2 to 46 gives us the third term:
\[ 23 \times 2 + 2 = 46 + 2 = 48 \]

### Step 4: Calculate the fourth term
- The third term is 48.
- If we multiply 48 by 2, we get 96.
- Adding 3 to 96 gives us the fourth term:
\[ 48 \times 2 + 3 = 96 + 3 = 99 \]

### Step 5: Calculate the fifth term (missing term)
- The fourth term is 99.
- If we multiply 99 by 2, we get 198.
- Adding 4 to 198 gives us the missing term:
\[ 99 \times 2 + 4 = 198 + 4 = 202 \]

### Step 6: Calculate the sixth term
- The missing term is 202.
- If we multiply 202 by 2, we get 404.
- Adding 5 to 404 gives us the sixth term:
\[ 202 \times 2 + 5 = 404 + 5 = 409 \]

### Conclusion
The missing term in the series is **202**.