What should come in place of the question mark (?) in the following number series?
`3" "4" "12" "?" "196`

Options

A. 45
B. 40
C. 41
D. 49

Answer

To solve the number series: `3, 4, 12, ?, 196`, we will look for a pattern in the numbers.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The series starts with 3 and goes to 4. Let's analyze how we can get from 3 to 4.
- From 3 to 4:
\[ 3 \times 1 + 1 = 4 \]

2. **Next Step**:
- Now, let's see how we can get from 4 to 12.
- From 4 to 12:
\[ 4 \times 2 + 4 = 12 \]

3. **Continuing the Pattern**:
- Next, we need to find the missing number (?). We will use the same pattern.
- From 12 to ?:
\[ 12 \times 3 + 9 = ? \]
- Here, we multiply by 3 and add \(3^2 = 9\).
- So, calculate:
\[ 12 \times 3 = 36 \]
\[ 36 + 9 = 45 \]
- Therefore, the missing number is 45.

4. **Final Step**:
- Now, let's confirm the next step to ensure the pattern holds.
- From 45 to 196:
\[ 45 \times 4 + 16 = 196 \]
- Here, we multiply by 4 and add \(4^2 = 16\).
- Calculate:
\[ 45 \times 4 = 180 \]
\[ 180 + 16 = 196 \]
- This confirms that our pattern is consistent.

### Conclusion:
The missing number in the series is **45**.