22 10 8 12 40 ?

Options

A. 304
B. 634
C. 264
D. 164

Explanation

To solve the series: 22, 10, 8, 12, 40, ?, we need to identify the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the first transformation**:
- Start with 22. To get to 10, we can multiply 22 by 0.5 (which is the same as dividing by 2) and then subtract 1.
- Calculation:
\[ 22 \times 0.5 = 11 \quad \text{then} \quad 11 - 1 = 10 \]

2. **Identify the second transformation**:
- Now, from 10 to 8, we can multiply 10 by 1 and subtract 2.
- Calculation:
\[ 10 \times 1 = 10 \quad \text{then} \quad 10 - 2 = 8 \]

3. **Identify the third transformation**:
- Next, from 8 to 12, we multiply 8 by 2 and then subtract 4.
- Calculation:
\[ 8 \times 2 = 16 \quad \text{then} \quad 16 - 4 = 12 \]

4. **Identify the fourth transformation**:
- From 12 to 40, we multiply 12 by 4 and then subtract 8.
- Calculation:
\[ 12 \times 4 = 48 \quad \text{then} \quad 48 - 8 = 40 \]

5. **Identify the pattern**:
- The pattern we see is multiplying by a factor that doubles each time (0.5, 1, 2, 4) and subtracting an increasing even number (1, 2, 4, 8).
- The next multiplication factor should be 8 (double of 4), and we will subtract 16 (double of 8).

6. **Calculate the next number**:
- Now, we take 40, multiply it by 8, and then subtract 16.
- Calculation:
\[ 40 \times 8 = 320 \quad \text{then} \quad 320 - 16 = 304 \]

### Final Answer:
The next number in the series is **304**.