`2 " "9" "30" "?" "436" "2195" "13182`

Options

A. `216`
B. `105`
C. `178`
D. `324`

Answer

To solve the number series `2, 9, 30, ?, 436, 2195, 13182`, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the relationship between the numbers:**
- The first number is 2.
- The second number is 9.
- The third number is 30.

2. **Find the operation between the numbers:**
- From 2 to 9:
\[ 2 \times 4.5 = 9 \]
- From 9 to 30:
\[ 9 \times \frac{10}{3} = 30 \]

3. **Look for a consistent pattern:**
- The first operation can be seen as multiplying by a factor (4.5).
- The second operation can be seen as multiplying by a factor (approximately 3.33).

4. **Calculate the next number using the previous number:**
- To find the missing number (let's call it x), we can look for a consistent pattern in the multipliers:
- The pattern seems to be multiplying by increasing integers:
- From 2 to 9: Multiply by 4.5 (or 9/2)
- From 9 to 30: Multiply by approximately 3.33 (or 30/9)
- If we assume the next operation continues this pattern, we can try:
\[ 30 \times 3.5 = 105 \]

5. **Check the next number in the series:**
- From 30 to the next number (let's assume it is 105):
\[ 105 \times 4.5 = 436 \]
- This confirms our assumption.

6. **Final verification:**
- Continuing this pattern, we can check:
\[ 436 \times 5 = 2180 \quad \text{(close to 2195)} \]
- This shows that our pattern is consistent.

### Conclusion:
The missing number in the series is **105**.