1 2 6 21 ? 445 2676

Options

A. 88
B. 77
C. 52
D. 64

Explanation

To solve the series: 1, 2, 6, 21, ?, 445, 2676, we need to identify the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The first number is 1.
- The second number is 2, which can be obtained by multiplying the first number (1) by 1 and adding 1:
\[ 1 \times 1 + 1 = 2 \]

2. **Continue the Pattern**:
- The third number is 6. We can get this by taking the second number (2) and multiplying it by 2, then adding 2:
\[ 2 \times 2 + 2 = 6 \]

3. **Next Number**:
- The fourth number is 21. We can find this by taking the third number (6) and multiplying it by 3, then adding 3:
\[ 6 \times 3 + 3 = 21 \]

4. **Find the Missing Number**:
- Now we need to find the next number in the series. We take the fourth number (21) and multiply it by 4, then add 4:
\[ 21 \times 4 + 4 = 84 + 4 = 88 \]
- So, the missing number is 88.

5. **Continue the Pattern to Verify**:
- The next number after 88 should be calculated as follows:
\[ 88 \times 5 + 5 = 440 + 5 = 445 \]
- This matches the next number in the series.

6. **Final Verification**:
- Continuing further, we can check:
\[ 445 \times 6 + 6 = 2670 + 6 = 2676 \]
- This also matches the given series.

### Conclusion:
The missing number in the series is **88**.