9 19 40 83 ? 345 696

Options

A. 162
B. 170
C. 175
D. 166

Explanation

To find the missing number in the series: 9, 19, 40, 83, ?, 345, 696, we will analyze the pattern in the series step by step.

### Step-by-Step Solution:

1. **Identify the Pattern**:
- The series is: 9, 19, 40, 83, ?, 345, 696.
- We need to find the missing number between 83 and 345.

2. **Calculate the Differences**:
- From 9 to 19:
\[ 19 = 9 \times 2 + 1 \]
- From 19 to 40:
\[ 40 = 19 \times 2 + 2 \]
- From 40 to 83:
\[ 83 = 40 \times 2 + 3 \]

3. **Establish the Next Operation**:
- Following the pattern, the next operation should be:
\[ \text{Next Number} = 83 \times 2 + 4 \]

4. **Perform the Calculation**:
- Calculate:
\[ 83 \times 2 = 166 \]
- Then add 4:
\[ 166 + 4 = 170 \]

5. **Confirm the Next Number in the Series**:
- Now we check if this fits the next number in the series:
\[ 170 \times 2 + 5 = 340 + 5 = 345 \]
- This confirms that our calculation is correct.

6. **Final Result**:
- The missing number in the series is **170**.

### Summary:
The missing number in the series 9, 19, 40, 83, ?, 345, 696 is **170**.