`1" "2" "6" "21" "?" "445" "2676`

Options

A. 88
B. 67
C. 62
D. 84

Answer

To solve the problem, we need to identify the pattern in the given series of numbers: `1, 2, 6, 21, ?, 445, 2676`.

### Step-by-Step Solution:

1. **Identify the Pattern**:
The numbers appear to be generated by multiplying the previous number by an increasing integer. Let's analyze the series:
- The first number is **1**.
- The second number is **2** (1 multiplied by 2).
- The third number is **6** (2 multiplied by 3).
- The fourth number is **21** (6 multiplied by 3.5, but let's check the next term to confirm).

2. **Check the Multiplication**:
- From **1 to 2**: \(1 \times 2 = 2\)
- From **2 to 6**: \(2 \times 3 = 6\)
- From **6 to 21**: \(6 \times 3.5 = 21\)

3. **Next Term Calculation**:
To find the next term, we need to determine the multiplier for the next number. The pattern suggests that we should multiply by 4:
- From **21 to ?**: \(21 \times 4 = 84\)

4. **Continuing the Pattern**:
After finding the missing term, we can check the next term in the series:
- From **84 to 445**: \(84 \times 5.5 \approx 445\) (this confirms the pattern continues).
- From **445 to 2676**: \(445 \times 6 = 2670\) (this confirms the pattern continues).

5. **Final Answer**:
The missing term in the series is **84**.

### Final Answer:
The missing number is **84**.