what should come in place of question mark( ?) in the following number series ?
`12" "14" "32" "102" "416" "2090" "?`

Options

A. 15522
B. 12552
C. 13525
D. 17552

Answer

To solve the number series: `12, 14, 32, 102, 416, 2090, ?`, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- Look at the first two numbers: 12 and 14.
- To get from 12 to 14, we can use the formula:
\[ 12 \times 1 + 2 = 14 \]

2. **Continue the Pattern**:
- Now, let's move to the next pair: 14 and 32.
- To get from 14 to 32, we can use:
\[ 14 \times 2 + 4 = 32 \]

3. **Next Pair**:
- Now, consider 32 and 102.
- To get from 32 to 102, we can use:
\[ 32 \times 3 + 6 = 102 \]

4. **Next Pair**:
- Now, look at 102 and 416.
- To get from 102 to 416, we can use:
\[ 102 \times 4 + 8 = 416 \]

5. **Next Pair**:
- Now, consider 416 and 2090.
- To get from 416 to 2090, we can use:
\[ 416 \times 5 + 10 = 2090 \]

6. **Final Calculation**:
- Now, we need to find the next number in the series after 2090.
- Following the established pattern, we will multiply by 6 and add 12:
\[ 2090 \times 6 + 12 \]
- Calculate \( 2090 \times 6 \):
\[ 2090 \times 6 = 12540 \]
- Now add 12:
\[ 12540 + 12 = 12552 \]

### Conclusion:
The number that should come in place of the question mark (?) is **12552**.