10.5 ? 15.75 31.5 78.75

Options

A. 10.5
B. 11.5
C. 12.5
D. 10.25

Explanation

To find the missing number in the series: 10.5, ?, 15.75, 31.5, 78.75, we will analyze the pattern in the series step by step.

### Step 1: Identify the given numbers in the series
The series is:
- First term: 10.5
- Second term: ?
- Third term: 15.75
- Fourth term: 31.5
- Fifth term: 78.75

### Step 2: Find the relationship between the terms
We will look for a pattern by examining the ratios of consecutive terms.

1. **From 31.5 to 78.75**:
\[ \frac{78.75}{31.5} = 2.5 \]

2. **From 15.75 to 31.5**:
\[ \frac{31.5}{15.75} = 2 \]

3. **From 10.5 to 15.75**:
To find the missing term, we can check the ratio:
\[ \frac{15.75}{10.5} = 1.5 \]

### Step 3: Calculate the missing term
Now, we can find the missing term by multiplying the first term (10.5) by the ratio (1.5):
\[ \text{Missing term} = 10.5 \times 1.5 = 15.75 \]

### Step 4: Verify the pattern
Now we can verify the entire series:
- 10.5 (first term)
- 15.75 (calculated missing term)
- 31.5 (15.75 × 2)
- 78.75 (31.5 × 2.5)

The pattern holds true, confirming that the missing term is indeed 15.75.

### Conclusion
The complete series is:
10.5, **15.75**, 15.75, 31.5, 78.75.