30 16 10 8 8 9 ?

Options

A. 12.75
B. 13
C. 14
D. 10.5

Explanation

To find the missing number in the series: 30, 16, 10, 8, 8, 9, ?, we can analyze the pattern step by step.

### Step 1: Identify the pattern
We observe that the series appears to be decreasing, and we can try to identify a consistent operation applied to each number.

### Step 2: Analyze the transitions between numbers
1. **From 30 to 16**:
- \(30 \div 2 = 15\)
- Then we add \(1\): \(15 + 1 = 16\)

2. **From 16 to 10**:
- \(16 \div 2 = 8\)
- Then we add \(2\): \(8 + 2 = 10\)

3. **From 10 to 8**:
- \(10 \div 2 = 5\)
- Then we add \(3\): \(5 + 3 = 8\)

4. **From 8 to 8**:
- \(8 \div 2 = 4\)
- Then we add \(4\): \(4 + 4 = 8\)

5. **From 8 to 9**:
- \(8 \div 2 = 4\)
- Then we add \(5\): \(4 + 5 = 9\)

### Step 3: Predict the next number
Following the established pattern, we now need to find the next number after 9:
- **From 9 to ?**:
- \(9 \div 2 = 4.5\)
- Then we add \(6\): \(4.5 + 6 = 10.5\)

### Conclusion
The missing number in the series is **10.5**.