568 ? 136 64 28 10 1

Options

A. 280
B. 240
C. 225
D. 174

Explanation

To solve the series: 568, ?, 136, 64, 28, 10, 1, we need to identify the pattern in the series.

### Step-by-Step Solution:

1. **Identify the Pattern**:
We notice that the numbers in the series are decreasing. To find the missing number, we will analyze the numbers that follow it.

2. **Analyze the Last Number**:
Starting from the last number in the series, which is 1, we can see how we can reach 10.
- To go from 1 to 10:
- We can use the formula: \(1 \times 2 + 8 = 10\).

3. **Continue the Pattern**:
Now, let's apply the same logic to find the next number:
- From 10 to 28:
- \(10 \times 2 + 8 = 20 + 8 = 28\).

4. **Next Step**:
Continuing this pattern:
- From 28 to 64:
- \(28 \times 2 + 8 = 56 + 8 = 64\).

5. **Next Step**:
- From 64 to 136:
- \(64 \times 2 + 8 = 128 + 8 = 136\).

6. **Finding the Missing Number**:
Now, we need to find the missing number that comes before 136:
- We reverse the pattern:
- Let the missing number be \(x\).
- We know \(x \times 2 + 8 = 136\).
- Rearranging gives us \(x \times 2 = 136 - 8\).
- Thus, \(x \times 2 = 128\).
- Therefore, \(x = \frac{128}{2} = 64\).

7. **Final Calculation**:
Now, we can find the missing number before 136:
- \(x = 136 \div 2 - 8 = 68 - 8 = 64\).

8. **Check the Previous Number**:
Finally, we can check the number before 64:
- \(64 \times 2 + 8 = 136\), which confirms our calculation.

Thus, the missing number in the series is **280**.

### Summary of the Pattern:
- The pattern is: Each number is obtained by multiplying the previous number by 2 and then adding 8.