Select the number that can replace the question mark (?) in the following series
1, 1, 2, 3, 7, 22, ?

Options

A. 152
B. 155
C. 157
D. 156

Answer

To solve the series: 1, 1, 2, 3, 7, 22, ?, we need to identify the pattern in the numbers.

### Step-by-Step Solution:

1. **Identify the Initial Numbers**: Start with the given series: 1, 1, 2, 3, 7, 22.

2. **Examine the Pattern**:
- The first two numbers are both 1.
- The third number (2) can be derived from the first two numbers: \(1 \times 1 + 1 = 2\).
- The fourth number (3) can be derived from the second number: \(1 \times 2 + 1 = 3\).
- The fifth number (7) can be derived from the third number: \(2 \times 3 + 1 = 7\).
- The sixth number (22) can be derived from the fourth number: \(3 \times 7 + 1 = 22\).

3. **Continue the Pattern**:
- Now, we need to find the next number after 22.
- Following the established pattern, we take the last number (22) and multiply it by the previous number (7) and then add 1:
\[ 22 \times 7 + 1 = 154 + 1 = 155 \]

4. **Conclusion**: The number that can replace the question mark (?) in the series is **155**.

### Final Answer:
The number that replaces the question mark (?) is **155**.