0.875 2.75 ? 18 40 85 176

Options

A. 7.5
B. 3.5
C. 5
D. 6.5

Explanation

To solve the series: 0.875, 2.75, ?, 18, 40, 85, 176, we need to identify the pattern in the sequence.

### Step-by-Step Solution:

1. **Identify the first two numbers**: The first number is 0.875 and the second number is 2.75.

2. **Find the relationship between the first two numbers**:
- Multiply the first number by 2 and add 1:
\[ 0.875 \times 2 + 1 = 1.75 + 1 = 2.75 \]
This confirms that the second number is derived from the first.

3. **Determine the next number in the series**:
- Now, apply the same pattern to find the missing number (let's call it \( x \)):
\[ x = 2.75 \times 2 + 2 \]
- Calculate:
\[ 2.75 \times 2 = 5.5 \]
\[ 5.5 + 2 = 7.5 \]
Thus, the missing number is 7.5.

4. **Continue the pattern to verify the subsequent numbers**:
- Next number after 7.5:
\[ 7.5 \times 2 + 3 = 15 + 3 = 18 \]
- Next number after 18:
\[ 18 \times 2 + 4 = 36 + 4 = 40 \]
- Next number after 40:
\[ 40 \times 2 + 5 = 80 + 5 = 85 \]
- Next number after 85:
\[ 85 \times 2 + 6 = 170 + 6 = 176 \]

5. **Conclusion**: The pattern holds true for all numbers in the series, confirming that the missing number is indeed 7.5.

### Final Answer:
The missing number in the series is **7.5**.

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