What will come in place of question mark (? ) in the following number series ?
` 435 " "354" "282" "219" "165" "?`

Options

A. 103
B. 112
C. 120
D. 130

Answer

To find the missing number in the series: `435, 354, 282, 219, 165, ?`, we will analyze the differences between consecutive terms step by step.

### Step 1: Calculate the differences between consecutive terms
- **First difference**:
\( 435 - 354 = 81 \)

- **Second difference**:
\( 354 - 282 = 72 \)

- **Third difference**:
\( 282 - 219 = 63 \)

- **Fourth difference**:
\( 219 - 165 = 54 \)

### Step 2: List the differences
Now we have the following differences:
- 81
- 72
- 63
- 54

### Step 3: Identify the pattern in the differences
The differences are decreasing by 9 each time:
- \( 81 - 9 = 72 \)
- \( 72 - 9 = 63 \)
- \( 63 - 9 = 54 \)

### Step 4: Find the next difference
Following the pattern, the next difference will be:
- \( 54 - 9 = 45 \)

### Step 5: Subtract the next difference from the last term
Now, we subtract this difference from the last known term in the series:
- \( 165 - 45 = 120 \)

### Conclusion
Thus, the missing number in the series is **120**.