8484, 4248, 2112, 1074, 513, 286.5, ?

Options

A. 136.25
B. 161.25
C. 107.25
D. 112.25

Explanation

To solve the series: 8484, 4248, 2112, 1074, 513, 286.5, ?, we will analyze the pattern step by step.

### Step 1: Identify the pattern
The numbers in the series are decreasing, suggesting a division operation might be involved.

### Step 2: Calculate the first operation
- Start with the first number: **8484**
- Divide by 2:
\[ 8484 \div 2 = 4242 \]
- The next number in the series is **4248**.
- To get from **4242** to **4248**, we add **6**:
\[ 4242 + 6 = 4248 \]

### Step 3: Calculate the second operation
- Now take the second number: **4248**
- Divide by 2:
\[ 4248 \div 2 = 2124 \]
- The next number in the series is **2112**.
- To get from **2124** to **2112**, we subtract **12**:
\[ 2124 - 12 = 2112 \]

### Step 4: Calculate the third operation
- Next, take **2112**.
- Divide by 2:
\[ 2112 \div 2 = 1056 \]
- The next number in the series is **1074**.
- To get from **1056** to **1074**, we add **18**:
\[ 1056 + 18 = 1074 \]

### Step 5: Calculate the fourth operation
- Now take **1074**.
- Divide by 2:
\[ 1074 \div 2 = 537 \]
- The next number in the series is **513**.
- To get from **537** to **513**, we subtract **24**:
\[ 537 - 24 = 513 \]

### Step 6: Calculate the fifth operation
- Next, take **513**.
- Divide by 2:
\[ 513 \div 2 = 256.5 \]
- The next number in the series is **286.5**.
- To get from **256.5** to **286.5**, we add **30**:
\[ 256.5 + 30 = 286.5 \]

### Step 7: Calculate the sixth operation
- Now take **286.5**.
- Divide by 2:
\[ 286.5 \div 2 = 143.25 \]
- To find the next number, we need to subtract **36** (the next increment in the pattern, which is 6 multiplied by 6):
\[ 143.25 - 36 = 107.25 \]

### Conclusion
The missing number in the series is **107.25**.