What should come in place of the question mark (?) in the following number series ?
`"2 13 67 ? 817 1639 1645"`

Options

A. 271
B. 205
C. 262
D. 218

Answer

To find the missing number in the series: 2, 13, 67, ?, 817, 1639, 1645, we will follow a pattern based on multiplication and addition.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The first number is 2.
- To get the second number (13), we multiply 2 by 6 and then add 1.
\[ 2 \times 6 + 1 = 12 + 1 = 13 \]

2. **Continue the Pattern**:
- To get the third number (67), we take the second number (13), multiply it by 5, and then add 2.
\[ 13 \times 5 + 2 = 65 + 2 = 67 \]

3. **Determine the Missing Number**:
- Now, we will find the fourth number (the question mark). We take the third number (67), multiply it by 4, and then add 3.
\[ 67 \times 4 + 3 = 268 + 3 = 271 \]

4. **Check the Next Numbers**:
- To verify the pattern, we can check the next numbers in the series.
- For the fifth number (817), we take the fourth number (271), multiply it by 3, and add 4.
\[ 271 \times 3 + 4 = 813 + 4 = 817 \]
- For the sixth number (1639), we take the fifth number (817), multiply it by 2, and add 5.
\[ 817 \times 2 + 5 = 1634 + 5 = 1639 \]
- For the seventh number (1645), we take the sixth number (1639), multiply it by 1, and add 6.
\[ 1639 \times 1 + 6 = 1639 + 6 = 1645 \]

5. **Final Answer**:
- The missing number in the series is 271.

### Conclusion:
The number that should come in place of the question mark (?) is **271**.